Lemma functors_eq_data_equiv_unitary_functors_eq_inv_law2 (u : is_univalent_dagger dagD) : ∏ y : unitary_functors_eq, functors_eq_data_to_unitary_functors_eq u (functors_eq_data_from_unitary_functors_eq u y) = y. Proof. intro p. use total2_paths_f. - apply funextsec ; intro. use total2_paths_f. + apply maponpaths, idtodaggeriso_daggerisotoid. + apply isaprop_is_unitary. - 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.