(** * Relating strict and large orders *)

Notation Zgt_iff_lt := Z.gt_lt_iff (only parsing).Notation Zge_iff_le := Z.ge_le_iff (only parsing).

(* Specifications: *)
Lemma Zle_not_lt n m : n <= m -> ~ m < n.
Lemma Zlt_not_le n m : n < m -> ~ m <= n.
Lemma Zle_not_gt n m : n <= m -> ~ n > m.
Lemma Zgt_not_le n m : n > m -> ~ n <= m.
Lemma Znot_ge_lt n m : ~ n >= m -> n < m.
Lemma Znot_lt_ge n m : ~ n < m -> n >= m.
Lemma Znot_gt_le n m: ~ n > m -> n <= m.
Lemma Znot_le_gt n m : ~ n <= m -> n > m.
Lemma not_Zne n m : ~ Zne n m -> n = m.