proposition: 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: Proof. rewrite to_commax'. rewrite (to_commax' _ g). apply to_binop_inv_comm_1. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Core.Functors