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. 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.
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.