proposition: Lemma to_inv_unel {x y : PA} : to_inv (to_unel x y) = to_unel x y.
proof: Proof. unfold to_unel. set (tmp := grinvunel (to_abgr x y)). cbn in tmp. unfold to_inv. apply tmp. 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