Lemma pre_comp_with_iso_is_inj {C : precategory_data} (a b c : ob C) (f : a --> b) (H : is_iso f) (g h : b --> c) : f · g = f · h -> g = h. Proof. intro X. apply (invmaponpathsweq (make_weq (precomp_with f) (H _ ))). apply X. 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.