proposition: Lemma PreAdditive_invrcomp {x y z : A} (f : A⟦x, y⟧) (g : A⟦y, z⟧) : (to_inv (f · g)) = f · (to_inv g).
proof: Proof. use (grrcan (to_abgr x z) (f · g)). unfold to_inv at 1. rewrite grlinvax. use (pathscomp0 _ (to_premor_linear' f (to_inv g) g)). rewrite linvax. rewrite to_premor_unel'. unfold to_unel. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels