Definition compare := O.compare.

(* Specifications: *)
Lemma compare_spec : forall x y, CompSpec eq lt x y (compare x y).
Definition eq_dec : forall x y, { eq x y } + { ~ eq x y }.
Lemma compare_Eq : forall x y, compare x y = Eq <-> eq x y.
Lemma compare_Lt : forall x y, compare x y = Lt <-> lt x y.
Lemma compare_Gt : forall x y, compare x y = Gt <-> lt y x.
Lemma compare_trans :
forall c x y z, (x?=y) = c -> (y?=z) = c -> (x?=z) = c.