proposition: Lemma abmonoidsbinop_runax {X Y : abmonoid} (f : monoidfun X Y) : abmonoidshombinop f (unelmonoidfun X Y) = f.
proof: Proof. use monoidfun_paths. use funextfun. intros x. use (runax Y). Qed.
imports: UniMath.Algebra.BinaryOperations UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders