(** 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 Zle_0_nat : forall n:nat, 0 <= Z.of_nat n.