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).
Notation mul_nonpos := le_mul_0 (only parsing).
Notation le_0_square := square_nonneg (only parsing).

Theorem lt_m1_mul_r : forall n m, n < -1 ->
n * m < -1 \/ n * m == 0 \/ 1 < n * m.