Lemma z_iso_inv_to_right {C : precategory} (a b c : ob C) (f : a --> b) (g : z_iso b c) (h : a --> c) : f = h · inv_from_z_iso g -> f · g = h. Proof. intro H. intermediate_path (h · inv_from_z_iso g · g). - rewrite H. apply idpath. - rewrite <- assoc, z_iso_after_z_iso_inv, id_right. apply idpath. Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories.