Lemma idtodaggermor_is_dagger_of_idtodaggermor {C : category} (dagC : dagger C) {x y : C} (p : x = y) : idtodaggermor dagC p = dagC y x (idtodaggermor dagC (! p)). Proof. induction p. apply pathsinv0, dagger_to_law_id. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DaggerCategories.Categories. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary.