(** ** Addition *)
(** Compatibility of addition wrt to order *)
Notation Zplus_le_lt_compat := Z.add_le_lt_mono (only parsing).
Notation Zplus_le_compat := Z.add_le_mono (only parsing).
Notation Zplus_lt_compat := Z.add_lt_mono (only parsing).

Lemma Zplus_lt_compat_r n m p : n < m -> n + p < m + p.
Notation Zplus_le_0_compat := Z.add_nonneg_nonneg (only parsing).