Module Backport_OT (O:OrderedType) <: OrderedTypeOrig.
Include Backport_DT O. (* Provides : t eq eq_refl eq_sym eq_trans eq_dec *)
Definition lt := O.lt.
Instance lt_strorder : StrictOrder lt.
Instance lt_compat : Proper (eq==>eq==>iff) lt.
Definition compare := O.compare.
Definition eq_dec : forall x y, { eq x y } + { ~ eq x y }.

Lemma compare_trans :
forall c x y z, (x?=y) = c -> (y?=z) = c -> (x?=z) = c.