Lemma z_iso_inv_on_right {C : precategory} (a b c : ob C) (f : z_iso a b) (g : b --> c) (h : a --> c) (H : h = f · g) : inv_from_z_iso f · h = g. Proof. assert (H2 : inv_from_z_iso f · h = inv_from_z_iso f · (f · g)). apply maponpaths; assumption. rewrite assoc in H2. rewrite H2. rewrite z_iso_after_z_iso_inv. apply id_left. 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.