(** Weakening order *)

Notation Zle_succ := Z.le_succ_diag_r (only parsing).Notation Zle_pred := Z.le_pred_l (only parsing).Notation Zlt_lt_succ := Z.lt_lt_succ_r (only parsing).Notation Zle_le_succ := Z.le_le_succ_r (only parsing).

Lemma Zlt_succ_pred n m : Z.succ n < m -> n < Z.pred m.