(** Special base instances of order *)
Notation Zlt_pred := Z.lt_pred_l (only parsing).

(* Specifications: *)
Lemma Zgt_succ n : Z.succ n > n.
Lemma Znot_le_succ n : ~ Z.succ n <= n.
(** Relating strict and large order using successor or predecessor *)
Lemma Zgt_le_succ n m : m > n -> Z.succ n <= m.
Lemma Zle_gt_succ n m : n <= m -> Z.succ m > n.
Lemma Zle_lt_succ n m : n <= m -> n < Z.succ m.
Lemma Zlt_le_succ n m : n < m -> Z.succ n <= m.
Lemma Zgt_succ_le n m : Z.succ m > n -> n <= m.
Lemma Zlt_succ_le n m : n < Z.succ m -> n <= m.
Lemma Zle_succ_gt n m : Z.succ n <= m -> m > n.
Notation Zle_succ := Z.le_succ_diag_r (only parsing).