Lemma inv_isotoid (C : category) (H : is_univalent C) (a b : C) (f : z_iso a b) : ! isotoid _ H f = isotoid _ H (z_iso_inv_from_z_iso f). Proof. apply idtoiso_inj; try assumption. rewrite idtoiso_isotoid. rewrite idtoiso_inv. rewrite idtoiso_isotoid. apply idpath. Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos.