(** Dichotomy *)
(** Transitivity of strict orders *)

(* Specifications: *)
Lemma Zgt_trans n m p : n > m -> m > p -> n > p.
(** Mixed transitivity *)
Lemma Zle_gt_trans n m p : m <= n -> m > p -> n > p.
Lemma Zgt_le_trans n m p : n > m -> p <= m -> n > p.
(** Transitivity of large orders *)
Lemma Zge_trans n m p : n >= m -> m >= p -> n >= p.
#[global]
Hint Resolve Z.le_trans: zarith.