proposition: Lemma idtoiso_of_pathsinv_is_dagger_of_idtoiso {C : category} (dagC : dagger C) {x y : C} (p : x = y) : pr1 (Univalence.idtoiso (! p)) = dagC x y (pr1 (Univalence.idtoiso p)).
proof: Proof. induction p. apply pathsinv0, dagger_to_law_id. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.DaggerCategories.Categories UniMath.CategoryTheory.DaggerCategories.Unitary