Lemma iscommrigdirprod (X Y : commrig) : iscommrigops (@op1 (setwith2binopdirprod X Y)) (@op2 (setwith2binopdirprod X Y)). Proof. intros. exists (isrigdirprod X Y). apply (pr2 (isabmonoiddirprod (commrigmultabmonoid X) (commrigmultabmonoid Y))). Defined.
Require Import UniMath.Algebra.Groups. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders.