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 lt_1_mul_pos : forall n m, 1 < n -> 0 < m -> 1 < n * m.