[class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (Type u_1) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (Type u_1) (@add_comm_monoid.to_add_monoid (Type u_1) (@semiring.to_add_comm_monoid (Type u_1) ?x_67)) (@mul_one_class.to_has_one (Type u_1) (@mul_zero_one_class.to_mul_one_class (Type u_1) (@monoid_with_zero.to_mul_zero_one_class (Type u_1) (@semiring.to_monoid_with_zero (Type u_1) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type u_1) (@add_comm_monoid.to_add_monoid (Type u_1) (@semiring.to_add_comm_monoid (Type u_1) ?x_67)) (@mul_one_class.to_has_one (Type u_1) (@mul_zero_one_class.to_mul_one_class (Type u_1) (@monoid_with_zero.to_mul_zero_one_class (Type u_1) (@semiring.to_monoid_with_zero (Type u_1) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type u_1) (@add_comm_monoid.to_add_monoid (Type u_1) (@semiring.to_add_comm_monoid (Type u_1) ?x_67)) (@mul_one_class.to_has_one (Type u_1) (@mul_zero_one_class.to_mul_one_class (Type u_1) (@monoid_with_zero.to_mul_zero_one_class (Type u_1) (@semiring.to_monoid_with_zero (Type u_1) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_1) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (Type u_1) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_1) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (Type u_1) [class_instances] caching failure for subsingleton (Type u_1) [class_instances] caching failure for subsingleton (Type u_1) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton α := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty α := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty α [class_instances] caching failure for subsingleton α [class_instances] caching failure for subsingleton α [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton 𝕜 := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p 𝕜 (@add_comm_monoid.to_add_monoid 𝕜 (@semiring.to_add_comm_monoid 𝕜 ?x_67)) (@mul_one_class.to_has_one 𝕜 (@mul_zero_one_class.to_mul_one_class 𝕜 (@monoid_with_zero.to_mul_zero_one_class 𝕜 (@semiring.to_monoid_with_zero 𝕜 ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p 𝕜 (@add_comm_monoid.to_add_monoid 𝕜 (@semiring.to_add_comm_monoid 𝕜 ?x_67)) (@mul_one_class.to_has_one 𝕜 (@mul_zero_one_class.to_mul_one_class 𝕜 (@monoid_with_zero.to_mul_zero_one_class 𝕜 (@semiring.to_monoid_with_zero 𝕜 ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p 𝕜 (@add_comm_monoid.to_add_monoid 𝕜 (@semiring.to_add_comm_monoid 𝕜 ?x_67)) (@mul_one_class.to_has_one 𝕜 (@mul_zero_one_class.to_mul_one_class 𝕜 (@monoid_with_zero.to_mul_zero_one_class 𝕜 (@semiring.to_monoid_with_zero 𝕜 ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton 𝕜 := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty 𝕜 := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty 𝕜 := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty 𝕜 [class_instances] caching failure for subsingleton 𝕜 [class_instances] caching failure for subsingleton 𝕜 [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (Type (max u_4 u_1)) (@add_comm_monoid.to_add_monoid (Type (max u_4 u_1)) (@semiring.to_add_comm_monoid (Type (max u_4 u_1)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_4 u_1)) (@mul_zero_one_class.to_mul_one_class (Type (max u_4 u_1)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_4 u_1)) (@semiring.to_monoid_with_zero (Type (max u_4 u_1)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type (max u_4 u_1)) (@add_comm_monoid.to_add_monoid (Type (max u_4 u_1)) (@semiring.to_add_comm_monoid (Type (max u_4 u_1)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_4 u_1)) (@mul_zero_one_class.to_mul_one_class (Type (max u_4 u_1)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_4 u_1)) (@semiring.to_monoid_with_zero (Type (max u_4 u_1)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type (max u_4 u_1)) (@add_comm_monoid.to_add_monoid (Type (max u_4 u_1)) (@semiring.to_add_comm_monoid (Type (max u_4 u_1)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_4 u_1)) (@mul_zero_one_class.to_mul_one_class (Type (max u_4 u_1)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_4 u_1)) (@semiring.to_monoid_with_zero (Type (max u_4 u_1)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (Type (max u_4 u_1)) [class_instances] caching failure for subsingleton (Type (max u_4 u_1)) [class_instances] caching failure for subsingleton (Type (max u_4 u_1)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) [class_instances] caching failure for subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) [class_instances] caching failure for subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ [class_instances] caching failure for subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ [class_instances] caching failure for subsingleton C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (Type (max u_4 u_1)) (@add_comm_monoid.to_add_monoid (Type (max u_4 u_1)) (@semiring.to_add_comm_monoid (Type (max u_4 u_1)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_4 u_1)) (@mul_zero_one_class.to_mul_one_class (Type (max u_4 u_1)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_4 u_1)) (@semiring.to_monoid_with_zero (Type (max u_4 u_1)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type (max u_4 u_1)) (@add_comm_monoid.to_add_monoid (Type (max u_4 u_1)) (@semiring.to_add_comm_monoid (Type (max u_4 u_1)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_4 u_1)) (@mul_zero_one_class.to_mul_one_class (Type (max u_4 u_1)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_4 u_1)) (@semiring.to_monoid_with_zero (Type (max u_4 u_1)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type (max u_4 u_1)) (@add_comm_monoid.to_add_monoid (Type (max u_4 u_1)) (@semiring.to_add_comm_monoid (Type (max u_4 u_1)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_4 u_1)) (@mul_zero_one_class.to_mul_one_class (Type (max u_4 u_1)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_4 u_1)) (@semiring.to_monoid_with_zero (Type (max u_4 u_1)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_4 u_1)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_4 u_1)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (Type (max u_4 u_1)) [class_instances] caching failure for subsingleton (Type (max u_4 u_1)) [class_instances] caching failure for subsingleton (Type (max u_4 u_1)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) [class_instances] caching failure for subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) [class_instances] caching failure for subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1 →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) [class_instances] caching failure for subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) [class_instances] caching failure for subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (nondiscrete_normed_field 𝕜) [class_instances] caching failure for subsingleton (nondiscrete_normed_field 𝕜) [class_instances] caching failure for subsingleton (nondiscrete_normed_field 𝕜) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (Type u_2) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (Type u_2) (@add_comm_monoid.to_add_monoid (Type u_2) (@semiring.to_add_comm_monoid (Type u_2) ?x_67)) (@mul_one_class.to_has_one (Type u_2) (@mul_zero_one_class.to_mul_one_class (Type u_2) (@monoid_with_zero.to_mul_zero_one_class (Type u_2) (@semiring.to_monoid_with_zero (Type u_2) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type u_2) (@add_comm_monoid.to_add_monoid (Type u_2) (@semiring.to_add_comm_monoid (Type u_2) ?x_67)) (@mul_one_class.to_has_one (Type u_2) (@mul_zero_one_class.to_mul_one_class (Type u_2) (@monoid_with_zero.to_mul_zero_one_class (Type u_2) (@semiring.to_monoid_with_zero (Type u_2) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type u_2) (@add_comm_monoid.to_add_monoid (Type u_2) (@semiring.to_add_comm_monoid (Type u_2) ?x_67)) (@mul_one_class.to_has_one (Type u_2) (@mul_zero_one_class.to_mul_one_class (Type u_2) (@monoid_with_zero.to_mul_zero_one_class (Type u_2) (@semiring.to_monoid_with_zero (Type u_2) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_2) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (Type u_2) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_2) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (Type u_2) [class_instances] caching failure for subsingleton (Type u_2) [class_instances] caching failure for subsingleton (Type u_2) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (normed_group E) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (normed_group E) [class_instances] caching failure for subsingleton (normed_group E) [class_instances] caching failure for subsingleton (normed_group E) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (Type u_3) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (Type u_3) (@add_comm_monoid.to_add_monoid (Type u_3) (@semiring.to_add_comm_monoid (Type u_3) ?x_67)) (@mul_one_class.to_has_one (Type u_3) (@mul_zero_one_class.to_mul_one_class (Type u_3) (@monoid_with_zero.to_mul_zero_one_class (Type u_3) (@semiring.to_monoid_with_zero (Type u_3) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type u_3) (@add_comm_monoid.to_add_monoid (Type u_3) (@semiring.to_add_comm_monoid (Type u_3) ?x_67)) (@mul_one_class.to_has_one (Type u_3) (@mul_zero_one_class.to_mul_one_class (Type u_3) (@monoid_with_zero.to_mul_zero_one_class (Type u_3) (@semiring.to_monoid_with_zero (Type u_3) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type u_3) (@add_comm_monoid.to_add_monoid (Type u_3) (@semiring.to_add_comm_monoid (Type u_3) ?x_67)) (@mul_one_class.to_has_one (Type u_3) (@mul_zero_one_class.to_mul_one_class (Type u_3) (@monoid_with_zero.to_mul_zero_one_class (Type u_3) (@semiring.to_monoid_with_zero (Type u_3) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_3) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (Type u_3) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_3) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (Type u_3) [class_instances] caching failure for subsingleton (Type u_3) [class_instances] caching failure for subsingleton (Type u_3) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space H) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space H) [class_instances] caching failure for subsingleton (topological_space H) [class_instances] caching failure for subsingleton (topological_space H) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (Type u_4) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (Type u_4) (@add_comm_monoid.to_add_monoid (Type u_4) (@semiring.to_add_comm_monoid (Type u_4) ?x_67)) (@mul_one_class.to_has_one (Type u_4) (@mul_zero_one_class.to_mul_one_class (Type u_4) (@monoid_with_zero.to_mul_zero_one_class (Type u_4) (@semiring.to_monoid_with_zero (Type u_4) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type u_4) (@add_comm_monoid.to_add_monoid (Type u_4) (@semiring.to_add_comm_monoid (Type u_4) ?x_67)) (@mul_one_class.to_has_one (Type u_4) (@mul_zero_one_class.to_mul_one_class (Type u_4) (@monoid_with_zero.to_mul_zero_one_class (Type u_4) (@semiring.to_monoid_with_zero (Type u_4) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type u_4) (@add_comm_monoid.to_add_monoid (Type u_4) (@semiring.to_add_comm_monoid (Type u_4) ?x_67)) (@mul_one_class.to_has_one (Type u_4) (@mul_zero_one_class.to_mul_one_class (Type u_4) (@monoid_with_zero.to_mul_zero_one_class (Type u_4) (@semiring.to_monoid_with_zero (Type u_4) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type u_4) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (Type u_4) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type u_4) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (Type u_4) [class_instances] caching failure for subsingleton (Type u_4) [class_instances] caching failure for subsingleton (Type u_4) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space M) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (normed_group E') := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (normed_group E') (@add_comm_monoid.to_add_monoid (normed_group E') (@semiring.to_add_comm_monoid (normed_group E') ?x_67)) (@mul_one_class.to_has_one (normed_group E') (@mul_zero_one_class.to_mul_one_class (normed_group E') (@monoid_with_zero.to_mul_zero_one_class (normed_group E') (@semiring.to_monoid_with_zero (normed_group E') ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E') (@add_comm_monoid.to_add_monoid (normed_group E') (@semiring.to_add_comm_monoid (normed_group E') ?x_67)) (@mul_one_class.to_has_one (normed_group E') (@mul_zero_one_class.to_mul_one_class (normed_group E') (@monoid_with_zero.to_mul_zero_one_class (normed_group E') (@semiring.to_monoid_with_zero (normed_group E') ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E') (@add_comm_monoid.to_add_monoid (normed_group E') (@semiring.to_add_comm_monoid (normed_group E') ?x_67)) (@mul_one_class.to_has_one (normed_group E') (@mul_zero_one_class.to_mul_one_class (normed_group E') (@monoid_with_zero.to_mul_zero_one_class (normed_group E') (@semiring.to_monoid_with_zero (normed_group E') ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (normed_group E') := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (normed_group E') [class_instances] caching failure for subsingleton (normed_group E') [class_instances] caching failure for subsingleton (normed_group E') [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space H') := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space H') (@add_comm_monoid.to_add_monoid (topological_space H') (@semiring.to_add_comm_monoid (topological_space H') ?x_67)) (@mul_one_class.to_has_one (topological_space H') (@mul_zero_one_class.to_mul_one_class (topological_space H') (@monoid_with_zero.to_mul_zero_one_class (topological_space H') (@semiring.to_monoid_with_zero (topological_space H') ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H') (@add_comm_monoid.to_add_monoid (topological_space H') (@semiring.to_add_comm_monoid (topological_space H') ?x_67)) (@mul_one_class.to_has_one (topological_space H') (@mul_zero_one_class.to_mul_one_class (topological_space H') (@monoid_with_zero.to_mul_zero_one_class (topological_space H') (@semiring.to_monoid_with_zero (topological_space H') ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H') (@add_comm_monoid.to_add_monoid (topological_space H') (@semiring.to_add_comm_monoid (topological_space H') ?x_67)) (@mul_one_class.to_has_one (topological_space H') (@mul_zero_one_class.to_mul_one_class (topological_space H') (@monoid_with_zero.to_mul_zero_one_class (topological_space H') (@semiring.to_monoid_with_zero (topological_space H') ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space H') := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space H') [class_instances] caching failure for subsingleton (topological_space H') [class_instances] caching failure for subsingleton (topological_space H') [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space M') := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space M') (@add_comm_monoid.to_add_monoid (topological_space M') (@semiring.to_add_comm_monoid (topological_space M') ?x_67)) (@mul_one_class.to_has_one (topological_space M') (@mul_zero_one_class.to_mul_one_class (topological_space M') (@monoid_with_zero.to_mul_zero_one_class (topological_space M') (@semiring.to_monoid_with_zero (topological_space M') ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M') (@add_comm_monoid.to_add_monoid (topological_space M') (@semiring.to_add_comm_monoid (topological_space M') ?x_67)) (@mul_one_class.to_has_one (topological_space M') (@mul_zero_one_class.to_mul_one_class (topological_space M') (@monoid_with_zero.to_mul_zero_one_class (topological_space M') (@semiring.to_monoid_with_zero (topological_space M') ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M') (@add_comm_monoid.to_add_monoid (topological_space M') (@semiring.to_add_comm_monoid (topological_space M') ?x_67)) (@mul_one_class.to_has_one (topological_space M') (@mul_zero_one_class.to_mul_one_class (topological_space M') (@monoid_with_zero.to_mul_zero_one_class (topological_space M') (@semiring.to_monoid_with_zero (topological_space M') ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space M') := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space M') [class_instances] caching failure for subsingleton (topological_space M') [class_instances] caching failure for subsingleton (topological_space M') [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@charted_space H' _inst_9 M' _inst_10) (@add_comm_monoid.to_add_monoid (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_add_comm_monoid (@charted_space H' _inst_9 M' _inst_10) ?x_67)) (@mul_one_class.to_has_one (@charted_space H' _inst_9 M' _inst_10) (@mul_zero_one_class.to_mul_one_class (@charted_space H' _inst_9 M' _inst_10) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_monoid_with_zero (@charted_space H' _inst_9 M' _inst_10) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H' _inst_9 M' _inst_10) (@add_comm_monoid.to_add_monoid (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_add_comm_monoid (@charted_space H' _inst_9 M' _inst_10) ?x_67)) (@mul_one_class.to_has_one (@charted_space H' _inst_9 M' _inst_10) (@mul_zero_one_class.to_mul_one_class (@charted_space H' _inst_9 M' _inst_10) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_monoid_with_zero (@charted_space H' _inst_9 M' _inst_10) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H' _inst_9 M' _inst_10) (@add_comm_monoid.to_add_monoid (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_add_comm_monoid (@charted_space H' _inst_9 M' _inst_10) ?x_67)) (@mul_one_class.to_has_one (@charted_space H' _inst_9 M' _inst_10) (@mul_zero_one_class.to_mul_one_class (@charted_space H' _inst_9 M' _inst_10) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_monoid_with_zero (@charted_space H' _inst_9 M' _inst_10) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@charted_space H' _inst_9 M' _inst_10) [class_instances] caching failure for subsingleton (@charted_space H' _inst_9 M' _inst_10) [class_instances] caching failure for subsingleton (@charted_space H' _inst_9 M' _inst_10) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, M; I', M'⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, M; I', M'⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, M; I', M'⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, M; I', M'⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, M; I', M'⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, M; I', M'⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, M; I', M'⟯ ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, M; I', M'⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, M; I', M'⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, M; I', M'⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, M; I', M'⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, M; I', M'⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, M; I', M'⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, M; I', M'⟯ ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, M; I', M'⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, M; I', M'⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, M; I', M'⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, M; I', M'⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, M; I', M'⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, M; I', M'⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, M; I', M'⟯ ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, M; I', M'⟯ := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, M; I', M'⟯ := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty C^⊤⟮I, M; I', M'⟯ [class_instances] caching failure for subsingleton C^⊤⟮I, M; I', M'⟯ [class_instances] caching failure for subsingleton C^⊤⟮I, M; I', M'⟯ [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton M := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty M := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty M [class_instances] caching failure for subsingleton M [class_instances] caching failure for subsingleton M [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (nondiscrete_normed_field 𝕜) [class_instances] caching failure for subsingleton (nondiscrete_normed_field 𝕜) [class_instances] caching failure for subsingleton (nondiscrete_normed_field 𝕜) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (normed_group E) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (normed_group E) [class_instances] caching failure for subsingleton (normed_group E) [class_instances] caching failure for subsingleton (normed_group E) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space H) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space H) [class_instances] caching failure for subsingleton (topological_space H) [class_instances] caching failure for subsingleton (topological_space H) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space M) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (normed_group E') := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (normed_group E') (@add_comm_monoid.to_add_monoid (normed_group E') (@semiring.to_add_comm_monoid (normed_group E') ?x_67)) (@mul_one_class.to_has_one (normed_group E') (@mul_zero_one_class.to_mul_one_class (normed_group E') (@monoid_with_zero.to_mul_zero_one_class (normed_group E') (@semiring.to_monoid_with_zero (normed_group E') ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E') (@add_comm_monoid.to_add_monoid (normed_group E') (@semiring.to_add_comm_monoid (normed_group E') ?x_67)) (@mul_one_class.to_has_one (normed_group E') (@mul_zero_one_class.to_mul_one_class (normed_group E') (@monoid_with_zero.to_mul_zero_one_class (normed_group E') (@semiring.to_monoid_with_zero (normed_group E') ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E') (@add_comm_monoid.to_add_monoid (normed_group E') (@semiring.to_add_comm_monoid (normed_group E') ?x_67)) (@mul_one_class.to_has_one (normed_group E') (@mul_zero_one_class.to_mul_one_class (normed_group E') (@monoid_with_zero.to_mul_zero_one_class (normed_group E') (@semiring.to_monoid_with_zero (normed_group E') ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E') := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (normed_group E') := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E') := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (normed_group E') [class_instances] caching failure for subsingleton (normed_group E') [class_instances] caching failure for subsingleton (normed_group E') [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E' (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_7) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space H') := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space H') (@add_comm_monoid.to_add_monoid (topological_space H') (@semiring.to_add_comm_monoid (topological_space H') ?x_67)) (@mul_one_class.to_has_one (topological_space H') (@mul_zero_one_class.to_mul_one_class (topological_space H') (@monoid_with_zero.to_mul_zero_one_class (topological_space H') (@semiring.to_monoid_with_zero (topological_space H') ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H') (@add_comm_monoid.to_add_monoid (topological_space H') (@semiring.to_add_comm_monoid (topological_space H') ?x_67)) (@mul_one_class.to_has_one (topological_space H') (@mul_zero_one_class.to_mul_one_class (topological_space H') (@monoid_with_zero.to_mul_zero_one_class (topological_space H') (@semiring.to_monoid_with_zero (topological_space H') ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H') (@add_comm_monoid.to_add_monoid (topological_space H') (@semiring.to_add_comm_monoid (topological_space H') ?x_67)) (@mul_one_class.to_has_one (topological_space H') (@mul_zero_one_class.to_mul_one_class (topological_space H') (@monoid_with_zero.to_mul_zero_one_class (topological_space H') (@semiring.to_monoid_with_zero (topological_space H') ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H') := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space H') := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H') := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space H') [class_instances] caching failure for subsingleton (topological_space H') [class_instances] caching failure for subsingleton (topological_space H') [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E' _inst_7 _inst_8 H' _inst_9) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space M') := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space M') (@add_comm_monoid.to_add_monoid (topological_space M') (@semiring.to_add_comm_monoid (topological_space M') ?x_67)) (@mul_one_class.to_has_one (topological_space M') (@mul_zero_one_class.to_mul_one_class (topological_space M') (@monoid_with_zero.to_mul_zero_one_class (topological_space M') (@semiring.to_monoid_with_zero (topological_space M') ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M') (@add_comm_monoid.to_add_monoid (topological_space M') (@semiring.to_add_comm_monoid (topological_space M') ?x_67)) (@mul_one_class.to_has_one (topological_space M') (@mul_zero_one_class.to_mul_one_class (topological_space M') (@monoid_with_zero.to_mul_zero_one_class (topological_space M') (@semiring.to_monoid_with_zero (topological_space M') ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M') (@add_comm_monoid.to_add_monoid (topological_space M') (@semiring.to_add_comm_monoid (topological_space M') ?x_67)) (@mul_one_class.to_has_one (topological_space M') (@mul_zero_one_class.to_mul_one_class (topological_space M') (@monoid_with_zero.to_mul_zero_one_class (topological_space M') (@semiring.to_monoid_with_zero (topological_space M') ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M') := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space M') := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M') := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space M') [class_instances] caching failure for subsingleton (topological_space M') [class_instances] caching failure for subsingleton (topological_space M') [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@charted_space H' _inst_9 M' _inst_10) (@add_comm_monoid.to_add_monoid (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_add_comm_monoid (@charted_space H' _inst_9 M' _inst_10) ?x_67)) (@mul_one_class.to_has_one (@charted_space H' _inst_9 M' _inst_10) (@mul_zero_one_class.to_mul_one_class (@charted_space H' _inst_9 M' _inst_10) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_monoid_with_zero (@charted_space H' _inst_9 M' _inst_10) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H' _inst_9 M' _inst_10) (@add_comm_monoid.to_add_monoid (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_add_comm_monoid (@charted_space H' _inst_9 M' _inst_10) ?x_67)) (@mul_one_class.to_has_one (@charted_space H' _inst_9 M' _inst_10) (@mul_zero_one_class.to_mul_one_class (@charted_space H' _inst_9 M' _inst_10) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_monoid_with_zero (@charted_space H' _inst_9 M' _inst_10) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H' _inst_9 M' _inst_10) (@add_comm_monoid.to_add_monoid (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_add_comm_monoid (@charted_space H' _inst_9 M' _inst_10) ?x_67)) (@mul_one_class.to_has_one (@charted_space H' _inst_9 M' _inst_10) (@mul_zero_one_class.to_mul_one_class (@charted_space H' _inst_9 M' _inst_10) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H' _inst_9 M' _inst_10) (@semiring.to_monoid_with_zero (@charted_space H' _inst_9 M' _inst_10) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H' _inst_9 M' _inst_10) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H' _inst_9 M' _inst_10) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@charted_space H' _inst_9 M' _inst_10) [class_instances] caching failure for subsingleton (@charted_space H' _inst_9 M' _inst_10) [class_instances] caching failure for subsingleton (@charted_space H' _inst_9 M' _inst_10) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, G; I, G⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, G; I, G⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, G; I, G⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, G; I, G⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, G; I, G⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, G; I, G⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, G; I, G⟯ ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, G; I, G⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, G; I, G⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, G; I, G⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, G; I, G⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, G; I, G⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, G; I, G⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, G; I, G⟯ ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p C^⊤⟮I, G; I, G⟯ (@add_comm_monoid.to_add_monoid C^⊤⟮I, G; I, G⟯ (@semiring.to_add_comm_monoid C^⊤⟮I, G; I, G⟯ ?x_67)) (@mul_one_class.to_has_one C^⊤⟮I, G; I, G⟯ (@mul_zero_one_class.to_mul_one_class C^⊤⟮I, G; I, G⟯ (@monoid_with_zero.to_mul_zero_one_class C^⊤⟮I, G; I, G⟯ (@semiring.to_monoid_with_zero C^⊤⟮I, G; I, G⟯ ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton C^⊤⟮I, G; I, G⟯ := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty C^⊤⟮I, G; I, G⟯ := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty C^⊤⟮I, G; I, G⟯ [class_instances] caching failure for subsingleton C^⊤⟮I, G; I, G⟯ [class_instances] caching failure for subsingleton C^⊤⟮I, G; I, G⟯ [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton G := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p G (@add_comm_monoid.to_add_monoid G (@semiring.to_add_comm_monoid G ?x_67)) (@mul_one_class.to_has_one G (@mul_zero_one_class.to_mul_one_class G (@monoid_with_zero.to_mul_zero_one_class G (@semiring.to_monoid_with_zero G ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p G (@add_comm_monoid.to_add_monoid G (@semiring.to_add_comm_monoid G ?x_67)) (@mul_one_class.to_has_one G (@mul_zero_one_class.to_mul_one_class G (@monoid_with_zero.to_mul_zero_one_class G (@semiring.to_monoid_with_zero G ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p G (@add_comm_monoid.to_add_monoid G (@semiring.to_add_comm_monoid G ?x_67)) (@mul_one_class.to_has_one G (@mul_zero_one_class.to_mul_one_class G (@monoid_with_zero.to_mul_zero_one_class G (@semiring.to_monoid_with_zero G ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton G := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty G := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty G := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty G [class_instances] caching failure for subsingleton G [class_instances] caching failure for subsingleton G [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (nondiscrete_normed_field 𝕜) [class_instances] caching failure for subsingleton (nondiscrete_normed_field 𝕜) [class_instances] caching failure for subsingleton (nondiscrete_normed_field 𝕜) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (normed_group E) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (normed_group E) [class_instances] caching failure for subsingleton (normed_group E) [class_instances] caching failure for subsingleton (normed_group E) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space H) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space H) [class_instances] caching failure for subsingleton (topological_space H) [class_instances] caching failure for subsingleton (topological_space H) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space M) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton M := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty M := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty M [class_instances] caching failure for subsingleton M [class_instances] caching failure for subsingleton M [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (nondiscrete_normed_field 𝕜) (@add_comm_monoid.to_add_monoid (nondiscrete_normed_field 𝕜) (@semiring.to_add_comm_monoid (nondiscrete_normed_field 𝕜) ?x_67)) (@mul_one_class.to_has_one (nondiscrete_normed_field 𝕜) (@mul_zero_one_class.to_mul_one_class (nondiscrete_normed_field 𝕜) (@monoid_with_zero.to_mul_zero_one_class (nondiscrete_normed_field 𝕜) (@semiring.to_monoid_with_zero (nondiscrete_normed_field 𝕜) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (nondiscrete_normed_field 𝕜) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (nondiscrete_normed_field 𝕜) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (nondiscrete_normed_field 𝕜) [class_instances] caching failure for subsingleton (nondiscrete_normed_field 𝕜) [class_instances] caching failure for subsingleton (nondiscrete_normed_field 𝕜) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (normed_group E) (@add_comm_monoid.to_add_monoid (normed_group E) (@semiring.to_add_comm_monoid (normed_group E) ?x_67)) (@mul_one_class.to_has_one (normed_group E) (@mul_zero_one_class.to_mul_one_class (normed_group E) (@monoid_with_zero.to_mul_zero_one_class (normed_group E) (@semiring.to_monoid_with_zero (normed_group E) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (normed_group E) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (normed_group E) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (normed_group E) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (normed_group E) [class_instances] caching failure for subsingleton (normed_group E) [class_instances] caching failure for subsingleton (normed_group E) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@add_comm_monoid.to_add_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_add_comm_monoid (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)) (@mul_one_class.to_has_one (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@mul_zero_one_class.to_mul_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@monoid_with_zero.to_mul_zero_one_class (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) (@semiring.to_monoid_with_zero (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] caching failure for subsingleton (@normed_space 𝕜 E (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) _inst_2) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space H) (@add_comm_monoid.to_add_monoid (topological_space H) (@semiring.to_add_comm_monoid (topological_space H) ?x_67)) (@mul_one_class.to_has_one (topological_space H) (@mul_zero_one_class.to_mul_one_class (topological_space H) (@monoid_with_zero.to_mul_zero_one_class (topological_space H) (@semiring.to_monoid_with_zero (topological_space H) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space H) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space H) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space H) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space H) [class_instances] caching failure for subsingleton (topological_space H) [class_instances] caching failure for subsingleton (topological_space H) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@add_comm_monoid.to_add_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_add_comm_monoid (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)) (@mul_one_class.to_has_one (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@mul_zero_one_class.to_mul_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@monoid_with_zero.to_mul_zero_one_class (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) (@semiring.to_monoid_with_zero (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] caching failure for subsingleton (@model_with_corners 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space M) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton M := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty M := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty M [class_instances] caching failure for subsingleton M [class_instances] caching failure for subsingleton M [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (topological_space M) (@add_comm_monoid.to_add_monoid (topological_space M) (@semiring.to_add_comm_monoid (topological_space M) ?x_67)) (@mul_one_class.to_has_one (topological_space M) (@mul_zero_one_class.to_mul_one_class (topological_space M) (@monoid_with_zero.to_mul_zero_one_class (topological_space M) (@semiring.to_monoid_with_zero (topological_space M) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (topological_space M) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (topological_space M) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (topological_space M) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] caching failure for subsingleton (topological_space M) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@charted_space H _inst_4 M _inst_5) (@add_comm_monoid.to_add_monoid (@charted_space H _inst_4 M _inst_5) (@semiring.to_add_comm_monoid (@charted_space H _inst_4 M _inst_5) ?x_67)) (@mul_one_class.to_has_one (@charted_space H _inst_4 M _inst_5) (@mul_zero_one_class.to_mul_one_class (@charted_space H _inst_4 M _inst_5) (@monoid_with_zero.to_mul_zero_one_class (@charted_space H _inst_4 M _inst_5) (@semiring.to_monoid_with_zero (@charted_space H _inst_4 M _inst_5) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@charted_space H _inst_4 M _inst_5) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@charted_space H _inst_4 M _inst_5) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] caching failure for subsingleton (@charted_space H _inst_4 M _inst_5) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton M := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p M (@add_comm_monoid.to_add_monoid M (@semiring.to_add_comm_monoid M ?x_67)) (@mul_one_class.to_has_one M (@mul_zero_one_class.to_mul_one_class M (@monoid_with_zero.to_mul_zero_one_class M (@semiring.to_monoid_with_zero M ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton M := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty M := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty M := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty M [class_instances] caching failure for subsingleton M [class_instances] caching failure for subsingleton M [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add α) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add α) [class_instances] caching failure for subsingleton (has_add α) [class_instances] caching failure for subsingleton (has_add α) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton α := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty α := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty α [class_instances] caching failure for subsingleton α [class_instances] caching failure for subsingleton α [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] caching failure for subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] caching failure for subsingleton (has_add (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (Type (max u_1 u_4)) (@add_comm_monoid.to_add_monoid (Type (max u_1 u_4)) (@semiring.to_add_comm_monoid (Type (max u_1 u_4)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_1 u_4)) (@mul_zero_one_class.to_mul_one_class (Type (max u_1 u_4)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_1 u_4)) (@semiring.to_monoid_with_zero (Type (max u_1 u_4)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type (max u_1 u_4)) (@add_comm_monoid.to_add_monoid (Type (max u_1 u_4)) (@semiring.to_add_comm_monoid (Type (max u_1 u_4)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_1 u_4)) (@mul_zero_one_class.to_mul_one_class (Type (max u_1 u_4)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_1 u_4)) (@semiring.to_monoid_with_zero (Type (max u_1 u_4)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (Type (max u_1 u_4)) (@add_comm_monoid.to_add_monoid (Type (max u_1 u_4)) (@semiring.to_add_comm_monoid (Type (max u_1 u_4)) ?x_67)) (@mul_one_class.to_has_one (Type (max u_1 u_4)) (@mul_zero_one_class.to_mul_one_class (Type (max u_1 u_4)) (@monoid_with_zero.to_mul_zero_one_class (Type (max u_1 u_4)) (@semiring.to_monoid_with_zero (Type (max u_1 u_4)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (Type (max u_1 u_4)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (Type (max u_1 u_4)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (Type (max u_1 u_4)) [class_instances] caching failure for subsingleton (Type (max u_1 u_4)) [class_instances] caching failure for subsingleton (Type (max u_1 u_4)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_lift_t a b) (@add_comm_monoid.to_add_monoid (has_lift_t a b) (@semiring.to_add_comm_monoid (has_lift_t a b) ?x_67)) (@mul_one_class.to_has_one (has_lift_t a b) (@mul_zero_one_class.to_mul_one_class (has_lift_t a b) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t a b) (@semiring.to_monoid_with_zero (has_lift_t a b) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_lift_t a b) (@add_comm_monoid.to_add_monoid (has_lift_t a b) (@semiring.to_add_comm_monoid (has_lift_t a b) ?x_67)) (@mul_one_class.to_has_one (has_lift_t a b) (@mul_zero_one_class.to_mul_one_class (has_lift_t a b) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t a b) (@semiring.to_monoid_with_zero (has_lift_t a b) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_lift_t a b) (@add_comm_monoid.to_add_monoid (has_lift_t a b) (@semiring.to_add_comm_monoid (has_lift_t a b) ?x_67)) (@mul_one_class.to_has_one (has_lift_t a b) (@mul_zero_one_class.to_mul_one_class (has_lift_t a b) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t a b) (@semiring.to_monoid_with_zero (has_lift_t a b) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t a b) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t a b) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_lift_t a b) [class_instances] caching failure for subsingleton (has_lift_t a b) [class_instances] caching failure for subsingleton (has_lift_t a b) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton a := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p a (@add_comm_monoid.to_add_monoid a (@semiring.to_add_comm_monoid a ?x_67)) (@mul_one_class.to_has_one a (@mul_zero_one_class.to_mul_one_class a (@monoid_with_zero.to_mul_zero_one_class a (@semiring.to_monoid_with_zero a ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p a (@add_comm_monoid.to_add_monoid a (@semiring.to_add_comm_monoid a ?x_67)) (@mul_one_class.to_has_one a (@mul_zero_one_class.to_mul_one_class a (@monoid_with_zero.to_mul_zero_one_class a (@semiring.to_monoid_with_zero a ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p a (@add_comm_monoid.to_add_monoid a (@semiring.to_add_comm_monoid a ?x_67)) (@mul_one_class.to_has_one a (@mul_zero_one_class.to_mul_one_class a (@monoid_with_zero.to_mul_zero_one_class a (@semiring.to_monoid_with_zero a ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton a := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty a := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty a := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty a [class_instances] caching failure for subsingleton a [class_instances] caching failure for subsingleton a [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] caching failure for subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] caching failure for subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@add_comm_monoid.to_add_monoid (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@semiring.to_add_comm_monoid (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) ?x_67)) (@mul_one_class.to_has_one (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@mul_zero_one_class.to_mul_one_class (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@monoid_with_zero.to_mul_zero_one_class (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@semiring.to_monoid_with_zero (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@add_comm_monoid.to_add_monoid (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@semiring.to_add_comm_monoid (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) ?x_67)) (@mul_one_class.to_has_one (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@mul_zero_one_class.to_mul_one_class (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@monoid_with_zero.to_mul_zero_one_class (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@semiring.to_monoid_with_zero (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@add_comm_monoid.to_add_monoid (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@semiring.to_add_comm_monoid (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) ?x_67)) (@mul_one_class.to_has_one (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@mul_zero_one_class.to_mul_one_class (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@monoid_with_zero.to_mul_zero_one_class (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@semiring.to_monoid_with_zero (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) [class_instances] caching failure for subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) [class_instances] caching failure for subsingleton (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) [class_instances] caching failure for subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) [class_instances] caching failure for subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) [class_instances] caching failure for subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) [class_instances] caching failure for subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1))) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add α) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add α) [class_instances] caching failure for subsingleton (has_add α) [class_instances] caching failure for subsingleton (has_add α) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton α := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty α := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty α [class_instances] caching failure for subsingleton α [class_instances] caching failure for subsingleton α [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@add_comm_monoid.to_add_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@semiring.to_add_comm_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) ?x_67)) (@mul_one_class.to_has_one (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@mul_zero_one_class.to_mul_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 … … G _inst_5 _inst_6 𝕜 … … … …)) … 𝕜 … … … …) …)) …))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@add_comm_monoid.to_add_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@semiring.to_add_comm_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) ?x_67)) (@mul_one_class.to_has_one (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@mul_zero_one_class.to_mul_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 … … G _inst_5 _inst_6 𝕜 … … … …)) … 𝕜 … … … …) …)) …))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@add_comm_monoid.to_add_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@semiring.to_add_comm_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) ?x_67)) (@mul_one_class.to_has_one (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@mul_zero_one_class.to_mul_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 … … G _inst_5 _inst_6 𝕜 … … … …)) … 𝕜 … … … …) …)) …))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) [class_instances] caching failure for subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) [class_instances] caching failure for subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y)))) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@add_comm_monoid.to_add_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@semiring.to_add_comm_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) ?x_67)) (@mul_one_class.to_has_one (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@mul_zero_one_class.to_mul_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@monoid_with_zero.to_mul_zero_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 …)) … G _inst_5 _inst_6 𝕜 … … … …)) … 𝕜 … … … …) …) …))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@add_comm_monoid.to_add_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@semiring.to_add_comm_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) ?x_67)) (@mul_one_class.to_has_one (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@mul_zero_one_class.to_mul_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@monoid_with_zero.to_mul_zero_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 …)) … G _inst_5 _inst_6 𝕜 … … … …)) … 𝕜 … … … …) …) …))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@add_comm_monoid.to_add_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@semiring.to_add_comm_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) ?x_67)) (@mul_one_class.to_has_one (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@mul_zero_one_class.to_mul_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) (@monoid_with_zero.to_mul_zero_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 …)) … G _inst_5 _inst_6 𝕜 … … … …)) … 𝕜 … … … …) …) …))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 [class_instances] (2) ?x_31 x : is_empty 𝕜 := @function.embedding.is_empty (?x_32 x) (?x_33 x) (?x_34 x) (?x_35 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := set.has_emptyc.emptyc.is_empty (?x_36 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := @sum.is_empty (?x_37 x) (?x_38 x) (?x_39 x) (?x_40 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := @psum.is_empty (?x_41 x) (?x_42 x) (?x_43 x) (?x_44 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := @prod.is_empty_right (?x_45 x) (?x_46 x) (?x_47 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := @prod.is_empty_left (?x_48 x) (?x_49 x) (?x_50 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := @pprod.is_empty_right (?x_51 x) (?x_52 x) (?x_53 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := @pprod.is_empty_left (?x_54 x) (?x_55 x) (?x_56 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := @pi.is_empty (?x_57 x) (?x_58 x) (?x_59 x) (?x_60 x) failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := fin.is_empty failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := false.is_empty failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := pempty.is_empty failed is_def_eq [class_instances] (2) ?x_31 x : is_empty 𝕜 := empty.is_empty failed is_def_eq [class_instances] caching failure for C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ → is_empty 𝕜 [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) [class_instances] caching failure for subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) [class_instances] caching failure for subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑X) + ⇑(fd (@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 1) ↑Y))) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 (⇑(@Lb 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8 g) 1)) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add α) (@add_comm_monoid.to_add_monoid (has_add α) (@semiring.to_add_comm_monoid (has_add α) ?x_67)) (@mul_one_class.to_has_one (has_add α) (@mul_zero_one_class.to_mul_one_class (has_add α) (@monoid_with_zero.to_mul_zero_one_class (has_add α) (@semiring.to_monoid_with_zero (has_add α) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add α) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add α) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add α) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add α) [class_instances] caching failure for subsingleton (has_add α) [class_instances] caching failure for subsingleton (has_add α) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton α := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p α (@add_comm_monoid.to_add_monoid α (@semiring.to_add_comm_monoid α ?x_67)) (@mul_one_class.to_has_one α (@mul_zero_one_class.to_mul_one_class α (@monoid_with_zero.to_mul_zero_one_class α (@semiring.to_monoid_with_zero α ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton α := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty α := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty α := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty α [class_instances] caching failure for subsingleton α [class_instances] caching failure for subsingleton α [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add 𝕜) (@add_comm_monoid.to_add_monoid (has_add 𝕜) (@semiring.to_add_comm_monoid (has_add 𝕜) ?x_67)) (@mul_one_class.to_has_one (has_add 𝕜) (@mul_zero_one_class.to_mul_one_class (has_add 𝕜) (@monoid_with_zero.to_mul_zero_one_class (has_add 𝕜) (@semiring.to_monoid_with_zero (has_add 𝕜) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add 𝕜) (@add_comm_monoid.to_add_monoid (has_add 𝕜) (@semiring.to_add_comm_monoid (has_add 𝕜) ?x_67)) (@mul_one_class.to_has_one (has_add 𝕜) (@mul_zero_one_class.to_mul_one_class (has_add 𝕜) (@monoid_with_zero.to_mul_zero_one_class (has_add 𝕜) (@semiring.to_monoid_with_zero (has_add 𝕜) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add 𝕜) (@add_comm_monoid.to_add_monoid (has_add 𝕜) (@semiring.to_add_comm_monoid (has_add 𝕜) ?x_67)) (@mul_one_class.to_has_one (has_add 𝕜) (@mul_zero_one_class.to_mul_one_class (has_add 𝕜) (@monoid_with_zero.to_mul_zero_one_class (has_add 𝕜) (@semiring.to_monoid_with_zero (has_add 𝕜) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add 𝕜) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add 𝕜) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add 𝕜) [class_instances] caching failure for subsingleton (has_add 𝕜) [class_instances] caching failure for subsingleton (has_add 𝕜) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@add_comm_monoid.to_add_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_add_comm_monoid (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)) (@mul_one_class.to_has_one (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@mul_zero_one_class.to_mul_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@monoid_with_zero.to_mul_zero_one_class (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_monoid_with_zero (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) [class_instances] caching failure for subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) [class_instances] caching failure for subsingleton (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _ →ₗ[𝕜] @point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@add_comm_monoid.to_add_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_add_comm_monoid (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)) (@mul_one_class.to_has_one (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@mul_zero_one_class.to_mul_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@monoid_with_zero.to_mul_zero_one_class (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) (@semiring.to_monoid_with_zero (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] caching failure for subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] caching failure for subsingleton (has_lift_t (@left_invariant_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 _inst_7 _inst_8) (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@add_comm_group.to_cancel_add_comm_monoid C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_add_comm_group 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@smooth_map_module' 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) (@smooth_map_module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@add_comm_monoid.to_add_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@semiring.to_add_comm_monoid (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) ?x_67)) (@mul_one_class.to_has_one (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@mul_zero_one_class.to_mul_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@monoid_with_zero.to_mul_zero_one_class (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) (@semiring.to_monoid_with_zero (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) [class_instances] caching failure for subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) [class_instances] caching failure for subsingleton (has_add (@point_derivation 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@add_comm_monoid.to_add_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@semiring.to_add_comm_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) ?x_67)) (@mul_one_class.to_has_one (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@mul_zero_one_class.to_mul_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@semiring.to_monoid_with_zero (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 …)) …) … …)) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@add_comm_monoid.to_add_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@semiring.to_add_comm_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) ?x_67)) (@mul_one_class.to_has_one (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@mul_zero_one_class.to_mul_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@semiring.to_monoid_with_zero (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 …)) …) … …)) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@add_comm_monoid.to_add_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@semiring.to_add_comm_monoid (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) ?x_67)) (@mul_one_class.to_has_one (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@mul_zero_one_class.to_mul_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@monoid_with_zero.to_mul_zero_one_class (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) (@semiring.to_monoid_with_zero (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 …)) …) … …)) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) [class_instances] caching failure for subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) [class_instances] caching failure for subsingleton (has_add (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y))) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@add_comm_monoid.to_add_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@semiring.to_add_comm_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) ?x_67)) (@mul_one_class.to_has_one (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@mul_zero_one_class.to_mul_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@monoid_with_zero.to_mul_zero_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@semiring.to_monoid_with_zero (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (… … 𝕜 … … … …) …) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@add_comm_monoid.to_add_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@semiring.to_add_comm_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) ?x_67)) (@mul_one_class.to_has_one (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@mul_zero_one_class.to_mul_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@monoid_with_zero.to_mul_zero_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@semiring.to_monoid_with_zero (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (… … 𝕜 … … … …) …) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@add_comm_monoid.to_add_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@semiring.to_add_comm_monoid (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) ?x_67)) (@mul_one_class.to_has_one (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@mul_zero_one_class.to_mul_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@monoid_with_zero.to_mul_zero_one_class (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) (@semiring.to_monoid_with_zero (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (… … 𝕜 … … … …) …) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 [class_instances] cached failure for C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ → is_empty 𝕜 [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) [class_instances] caching failure for subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) [class_instances] caching failure for subsingleton (@has_coe_to_fun.F (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@derivation.has_coe_to_fun 𝕜 (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑X + ⇑(@derivation.eval_at 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) ↑Y)) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@add_comm_monoid.to_add_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_add_comm_monoid (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)) (@mul_one_class.to_has_one (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@mul_zero_one_class.to_mul_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@monoid_with_zero.to_mul_zero_one_class (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) (@semiring.to_monoid_with_zero (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] caching failure for subsingleton (@derivation 𝕜 C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@comm_ring.to_comm_semiring 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))) (@comm_ring.to_comm_semiring C^⊤⟮I, G; 𝓘(𝕜, 𝕜), 𝕜⟯ (@smooth_map_comm_ring 𝕜 _inst_1 E _inst_2 _inst_3 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)) H _inst_4 I 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))))))) 𝓘(𝕜, 𝕜) G _inst_5 _inst_6 𝕜 (@semi_normed_comm_ring.to_comm_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_ring.to_pseudo_metric_space 𝕜 (@semi_normed_comm_ring.to_semi_normed_ring 𝕜 (@normed_comm_ring.to_semi_normed_comm_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@charted_space_self 𝕜 (@uniform_space.to_topological_space 𝕜 (@metric_space.to_uniform_space' 𝕜 (@semi_normed_group.to_pseudo_metric_space 𝕜 (@normed_group.to_semi_normed_group 𝕜 (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))))) _)) (@instances.smooth_functions_algebra 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6) 𝕜 (@add_comm_group.to_cancel_add_comm_monoid 𝕜 (@lie_ring.to_add_comm_group 𝕜 (@lie_ring.of_associative_ring 𝕜 (@normed_ring.to_ring 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))))))) (@point_derivation.module 𝕜 _inst_1 E _inst_2 _inst_3 H _inst_4 I G _inst_5 _inst_6 g) (@normed_space.to_module 𝕜 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1) (@normed_ring.to_normed_group 𝕜 (@normed_comm_ring.to_normed_ring 𝕜 (@normed_field.to_normed_comm_ring 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1)))) (@normed_field.to_normed_space 𝕜 (@nondiscrete_normed_field.to_normed_field 𝕜 _inst_1))) _) [class_instances] class-instance resolution trace [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_one failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_fin_zero failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @principal_seg.subsingleton ?x_1 ?x_2 ?x_3 ?x_4 ?x_5 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @initial_seg.subsingleton ?x_6 ?x_7 ?x_8 ?x_9 ?x_10 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @int_algebra_subsingleton ?x_11 ?x_12 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat_algebra_subsingleton ?x_13 ?x_14 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @matrix.subsingleton ?x_15 ?x_16 ?x_17 ?x_18 ?x_19 ?x_20 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @dmatrix.subsingleton ?x_21 ?x_22 ?x_23 ?x_24 ?x_25 ?x_26 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @rat.subsingleton_ring_hom ?x_27 ?x_28 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := fintype.subsingleton ?x_29 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @vector.zero_subsingleton ?x_30 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton' ?x_31 ?x_32 ?x_33 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @fin.order_iso_subsingleton ?x_34 ?x_35 ?x_36 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ring_hom.int.subsingleton_ring_hom ?x_37 ?x_38 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @nat.subsingleton_ring_hom ?x_39 ?x_40 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @invertible.subsingleton ?x_41 ?x_42 ?x_43 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @plift.subsingleton ?x_44 ?x_45 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @ulift.subsingleton ?x_46 ?x_47 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.perm_subsingleton ?x_48 ?x_49 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_dom ?x_50 ?x_51 ?x_52 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @equiv.equiv_subsingleton_cod ?x_53 ?x_54 ?x_55 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @order_dual.subsingleton ?x_56 ?x_57 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @unique.subsingleton_unique ?x_58 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @trunc.subsingleton ?x_59 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_pempty failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @subsingleton.prod ?x_60 ?x_61 ?x_62 ?x_63 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := empty.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := punit.subsingleton failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := decidable.subsingleton ?x_64 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := subsingleton_prop ?x_65 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @char_p.subsingleton ?x_66 ?x_67 ?x_68 [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @polynomial.char_p ?x_69 ?x_70 ?x_71 ?x_72 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @ring_char.char_p ?x_73 ?x_74 failed is_def_eq [class_instances] (1) ?x_68 : @char_p (has_coe_to_fun a) (@add_comm_monoid.to_add_monoid (has_coe_to_fun a) (@semiring.to_add_comm_monoid (has_coe_to_fun a) ?x_67)) (@mul_one_class.to_has_one (has_coe_to_fun a) (@mul_zero_one_class.to_mul_one_class (has_coe_to_fun a) (@monoid_with_zero.to_mul_zero_one_class (has_coe_to_fun a) (@semiring.to_monoid_with_zero (has_coe_to_fun a) ?x_67)))) 1 := @char_p.of_char_zero ?x_75 ?x_76 ?x_77 ?x_78 failed is_def_eq [class_instances] (0) ?x_0 : subsingleton (has_coe_to_fun a) := @is_empty.subsingleton ?x_1 ?x_2 [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @function.embedding.is_empty ?x_3 ?x_4 ?x_5 ?x_6 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := set.has_emptyc.emptyc.is_empty ?x_7 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @sum.is_empty ?x_8 ?x_9 ?x_10 ?x_11 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @psum.is_empty ?x_12 ?x_13 ?x_14 ?x_15 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_right ?x_16 ?x_17 ?x_18 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @prod.is_empty_left ?x_19 ?x_20 ?x_21 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_right ?x_22 ?x_23 ?x_24 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pprod.is_empty_left ?x_25 ?x_26 ?x_27 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := @pi.is_empty ?x_28 ?x_29 ?x_30 ?x_31 failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := fin.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := false.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := pempty.is_empty failed is_def_eq [class_instances] (1) ?x_2 : is_empty (has_coe_to_fun a) := empty.is_empty failed is_def_eq [class_instances] caching failure for is_empty (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a) [class_instances] caching failure for subsingleton (has_coe_to_fun a)