proposition: Lemma iscommringdirprod (X Y : commring) : iscommringops (@op1 (setwith2binopdirprod X Y)) (@op2 (setwith2binopdirprod X Y)).
proof: Proof. intros. split with (isringdirprod X Y). apply (pr2 (isabmonoiddirprod (ringmultabmonoid X) (ringmultabmonoid Y))). Defined.
imports: UniMath.Algebra.Groups UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.Algebra.Monoids