fact: Definition ismonoidfunisbinopfun {X Y : monoid} {f : X -> Y} (H : ismonoidfun f) : isbinopfun f := dirprod_pr1 H.
imports: UniMath.Algebra.BinaryOperations UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders