proposition: Lemma equality_equiv_functors_eq_data_inv_law2 : ∏ y : functors_eq_data, equality_to_functors_eq_data (equality_from_functors_eq_data y) = y.
proof: Proof. intros [p q]. use total2_paths_f. - apply funextsec ; intro. apply equality_on_objects_from_functor_equality. - apply proofirrelevance. do 3 (apply impred_isaprop ; intro). apply homset_property. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DaggerCategories.Categories UniMath.CategoryTheory.DaggerCategories.Unitary UniMath.CategoryTheory.DaggerCategories.Univalence UniMath.CategoryTheory.DaggerCategories.Functors UniMath.CategoryTheory.DaggerCategories.Transformations