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. 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.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DaggerCategories.Categories. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary. Require Import UniMath.CategoryTheory.DaggerCategories.Univalence. Require Import UniMath.CategoryTheory.DaggerCategories.Functors. Require Import UniMath.CategoryTheory.DaggerCategories.Transformations.