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 neq_mul_0 : forall n m, n ~= 0 /\ m ~= 0 <-> n * m ~= 0.