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 eq_mul_0_r : forall n m, n * m == 0 -> n ~= 0 -> m == 0.