Module Type ZMulOrderProp (Import Z : ZAxiomsMiniSig').
Include ZAddOrderProp Z.
Notation mul_pos := lt_0_mul (only parsing).
Notation mul_neg := lt_mul_0 (only parsing).
Notation mul_nonneg := le_0_mul (only parsing).

Theorem le_mul_0 :
forall n m, n * m <= 0 -> 0 <= n /\ m <= 0 \/ n <= 0 /\ 0 <= m.