Module Type NZMulOrderProp (Import NZ : NZOrdAxiomsSig').
Include NZAddOrderProp NZ.
(* There are still many variants of the theorem above. One can assume 0 < n or 0 < p or n <= m or p <= q. *)

Theorem mul_le_mono_nonneg :
forall n m p q, 0 <= n -> n <= m -> 0 <= p -> p <= q -> n * p <= m * q.