fact: Definition submonoidtosubsetswithbinop (X : monoid) : submonoid X -> @subsetswithbinop X := λ A : _, make_subsetswithbinop (pr1 A) (pr1 (pr2 A)).
imports: UniMath.Algebra.BinaryOperations UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders