Lemma abmonoidsbinop_lunax {X Y : abmonoid} (f : monoidfun X Y) : abmonoidshombinop (unelmonoidfun X Y) f = f. Proof. use monoidfun_paths. use funextfun. intros x. use (lunax Y). Qed.
Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.Monoids2.