(** ** Addition *)
(** Compatibility of addition wrt to order *)

Notation Zplus_lt_le_compat := Z.add_lt_le_mono (only parsing).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_le_compat_r n m p : n <= m -> n + p <= m + p.