Definition is_iso_qinv {C:precategory} {a b : C} (f : a --> b) (g : b --> a) : is_inverse_in_precat f g -> is_iso f. Proof. intros H c. apply (isweq_iso _ (precomp_with g)). - intro h. unfold precomp_with. rewrite assoc. apply remove_id_left. apply (pr2 H). apply idpath. - intro h. unfold precomp_with. rewrite assoc. apply remove_id_left. apply (pr1 H). apply idpath. 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.