fact: Definition subringtosubsetswith2binop (X : ring) : subring X -> @subsetswith2binop X := λ A : _, make_subsetswith2binop (pr1 A) (make_dirprod (pr1 (pr1 (pr1 (pr2 A)))) (pr1 (pr2 (pr2 A)))).
imports: UniMath.Algebra.Groups UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.Algebra.Monoids