proposition: Lemma iscommdirprod (X Y : abmonoid) : iscomm (@op (setwithbinopdirprod X Y)).
proof: Proof. intros xy xy'. destruct xy as [ x y ]. destruct xy' as [ x' y' ]. simpl. apply pathsdirprod. - apply (commax X). - apply (commax Y). Defined.
imports: UniMath.Algebra.BinaryOperations UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders