(** 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).

Lemma Zmult_gt_0_compat n m : n > 0 -> m > 0 -> n * m > 0.