Lemma cancel_precomposition_z_iso {C : precategory} {a b c : C} (f : z_iso a b) (g h : b --> c) : f · g = f · h -> g = h. Proof. use pre_comp_with_z_iso_is_inj. - exact (pr1 (pr2 f)). - exact (pr2 (pr2 f)). 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.