Module Update_OT (O:OrderedTypeOrig) <: OrderedType.
Include Update_DT O.  (* Provides : t eq eq_equiv eq_dec *)
Definition lt := O.lt.
Instance lt_strorder : StrictOrder lt.
Instance lt_compat : Proper (eq==>eq==>iff) lt.
Definition compare x y :=
match O.compare x y with
| EQ _ => Eq
| LT _ => Lt
| GT _ => Gt
end.

Lemma compare_spec : forall x y, CompSpec eq lt x y (compare x y).