Module OrderTac := OTF_to_OrderTac O.Ltac order := OrderTac.order.Ltac iorder := intuition order.#[global]
 Instance le_compat : Proper (eq==>eq==>iff) le.#[global]
 Instance le_preorder : PreOrder le.#[global]
 Instance le_order : PartialOrder eq le.#[global]
 Instance le_antisym : Antisymmetric _ eq le.

(* Specifications: *)
Lemma le_not_gt_iff : forall x y, x<=y <-> ~y<x.
Lemma lt_not_ge_iff : forall x y, x<y <-> ~y<=x.
Lemma le_or_gt : forall x y, x<=y \/ y<x.
Lemma lt_or_ge : forall x y, x<y \/ y<=x.
Lemma eq_is_le_ge : forall x y, x==y <-> x<=y /\ y<=x.
Lemma compare_le_iff x y : compare x y <> Gt <-> x<=y.
Lemma compare_ge_iff x y : compare x y <> Lt <-> y<=x.