Definition equality_from_functors_eq_data : functors_eq_data → pr1 F = pr1 G. Proof. intros [p q]. use total2_paths_f. - apply funextsec ; intro ; apply p. - abstract( repeat (apply funextsec ; intro) ; rewrite transport_of_dagger_functor_map_is_pointwise ; rewrite double_transport_idtodaggeriso ; rewrite toforallpaths_funextsec ; exact (! q _ _ _) ). Defined.
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.