(** 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).

(** ** Square *)
(** Simplification of square wrt order *)
Lemma Zlt_square_simpl n m : 0 <= n -> m * m < n * n -> m < n.