fact: Definition rigtoringop1int (X : rig) : binop (X × X) := λ x x', make_dirprod ((pr1 x) + (pr1 x')) ((pr2 x) + (pr2 x')).
imports: UniMath.Algebra.Groups UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.Algebra.Monoids