Lemma to_binop_inv_comm_2 {x y : PA} (f g : PA⟦x, y⟧) : to_binop _ _ f (to_inv g) = to_inv (to_binop _ _ (to_inv f) g). Proof. rewrite to_commax'. rewrite (to_commax' _ g). apply to_binop_inv_comm_1. 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.