Lemma functors_eq_data_equiv_unitary_functors_eq_inv_law1 (u : is_univalent_dagger dagD) : ∏ x : functors_eq_data, functors_eq_data_from_unitary_functors_eq u (functors_eq_data_to_unitary_functors_eq u x) = x. Proof. intro p. use total2_paths_f. - apply funextsec ; intro. apply daggerisotoid_idtodaggeriso. - repeat (apply funextsec ; 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.