proposition: Lemma equality_equiv_functors_eq_data_inv_law1 : ∏ x : pr1 F = pr1 G, equality_from_functors_eq_data (equality_to_functors_eq_data x) = x.
proof: Proof. intro. apply functor_eq_eq_from_functor_ob_eq'. refine (base_total2_paths _ @ _). apply (invmaponpathsweq (weqtoforallpaths _ _ _)). simpl. rewrite toforallpaths_funextsec. apply funextsec; intro ; apply idpath. 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