Lemma cancel_inv {x y : PA} (f g : PA⟦x, y⟧) (H : (to_inv f) = (to_inv g)) : f = g. Proof. apply (grinvmaponpathsinv (to_abgr x y) H). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Core.Functors.