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