fact: Definition opposite_commring (X : commring) : commring := ((pr1 (X⁰)),, (make_dirprod (pr2 (X⁰)) (fun x y => @ringcomm2 X y x))).
imports: UniMath.Algebra.Groups UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.Algebra.Monoids