#[global]
Hint Resolve Z.le_le_succ_r: zarith.
(** Relating order wrt successor and order wrt predecessor *)

(* Specifications: *)
Lemma Zgt_succ_pred n m : m > Z.succ n -> Z.pred m > n.
Lemma Zlt_succ_pred n m : Z.succ n < m -> n < Z.pred m.
(** Relating strict order and large order on positive *)
Lemma Zlt_0_le_0_pred n : 0 < n -> 0 <= Z.pred n.
Lemma Zgt_0_le_0_pred n : n > 0 -> 0 <= Z.pred n.
(** Special cases of ordered integers *)
Lemma Zle_neg_pos : forall p q:positive, Zneg p <= Zpos q.
Lemma Zgt_pos_0 : forall p:positive, Zpos p > 0.
(* weaker but useful (in [Z.pow] for instance) *)
Lemma Zle_0_pos : forall p:positive, 0 <= Zpos p.
Lemma Zlt_neg_0 : forall p:positive, Zneg p < 0.
Lemma Zle_0_nat : forall n:nat, 0 <= Z.of_nat n.
#[global]
Hint Immediate Z.eq_le_incl: zarith.