(** 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 Zgt_square_simpl n m : n >= 0 -> n * n > m * m -> n > m.
Notation Zle_plus_swap := Z.le_add_le_sub_r (only parsing).