fact: Definition monoidfunmul {X Y : monoid} (f : monoidfun X Y) (x x' : X) : f (op x x') = op (f x) (f x') := pr1 (pr2 f) x x'.
imports: UniMath.Algebra.BinaryOperations UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders