Definition compare (s s':  t) : comparison :=
 compare' (proj1_sig s) (proj1_sig s').Definition lt (s s': t):  Prop :=
    compare s s' = Lt.

(* Specifications: *)
Lemma lt_strorder : StrictOrder lt.
Lemma lt_compat: Proper (eq ==> eq ==> iff) lt.
Lemma compare_spec : forall s s' : t, CompSpec eq lt s s' (compare s s').