Lemma cancel_precomposition_iso {C : precategory_data} {a b c : C} (f : iso a b) (g h : b --> c) : f · g = f · h -> g = h. Proof. apply (pre_comp_with_iso_is_inj _ _ _ (pr1 f) (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.