Lemma idtodagger_as_idtoiso_pointwise {x y : C} (p : x = y) : idtodaggeriso (GRP_dagger C) x y p = z_iso_is_unitary x y (idtoiso p). Proof. apply (unitary_eq (idtodaggeriso (GRP_dagger C) x y p) (univalence_to_dagger_univalence (idtoiso p))). induction p ; apply idpath. 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.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.DaggerCategories.Categories. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary. Require Import UniMath.CategoryTheory.DaggerCategories.Univalence.