Lemma is_iso_comp_of_isos {C : precategory} {a b c : ob C} (f : iso a b) (g : iso b c) : is_iso (f · g). Proof. simpl. intro d. set (T := twooutof3c (precomp_with g) (precomp_with f (c:=d)) (pr2 g d) (pr2 f _)). apply (isweqhomot' _ _ T). intro h. apply assoc. Defined.
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.