Lemma to_rcan {x y : PA} {f g : PA⟦x, y⟧} (h : PA⟦x, y⟧) : to_binop x y f h = to_binop x y g h -> f = g. Proof. intros H. apply (grrcan (to_abgr x y) h 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.