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_nonneg_cancel_r : forall n m, 0 < m -> (0 <= n*m <-> 0 <= n).