proposition: Lemma inv_inv_eq {x y : PA} (f : PA⟦x, y⟧) : to_inv (to_inv f) = f.
proof: Proof. unfold to_inv. apply (grinvinv (to_abgr x y) f). 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