Module MOT_to_OT (Import O : MiniOrderedType) <: OrderedType.
Include O.
Definition eq_dec : forall x y : t, {eq x y} + {~ eq x y}.
Instance lt_strorder : StrictOrder lt.
Instance lt_compat : Proper (eq==>eq==>iff) lt.

Lemma elim_compare_lt :
forall x y : t,
lt x y -> exists H : lt x y, compare x y = LT H.