Lemma iso_inv_to_left {C : precategory} (a b c : ob C) (f : iso a b) (g : b --> c) (h : a --> c) : inv_from_iso f · h = g -> h = f · g. Proof. intro H. intermediate_path (f · inv_from_iso f · h). - rewrite iso_inv_after_iso, id_left; apply idpath. - rewrite <- assoc. rewrite H. 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.