(** Compatibility of multiplication by a positive wrt to being positive *)
Notation Zmult_le_0_compat := Z.mul_nonneg_nonneg (only parsing).
Notation Zmult_lt_0_compat := Z.mul_pos_pos (only parsing).
Notation Zmult_lt_O_compat := Z.mul_pos_pos (only parsing).

(** Simplification of multiplication by a positive wrt to being positive *)
Lemma Zmult_le_0_reg_r n m : n > 0 -> 0 <= m * n -> 0 <= m.