(** Simplification of successor wrt to order *)

(* Specifications: *)
Lemma Zsucc_gt_reg n m : Z.succ m > Z.succ n -> m > n.
Lemma Zsucc_le_reg n m : Z.succ m <= Z.succ n -> m <= n.
Lemma Zsucc_lt_reg n m : Z.succ n < Z.succ m -> n < m.
Notation Zlt_succ := Z.lt_succ_diag_r (only parsing).