Definition lt' (s s': tree):  Prop :=  compare' s s' = Lt.

(* Specifications: *)
Lemma lt'_strorder : StrictOrder lt'.
Lemma lt'_compat: Proper (eq ==> eq ==> iff) lt'.
Lemma min_elt'_spec2: forall s (x : key) (y : key), choose' s = Some x -> interp s y -> forall (lo hi : option key) (ST: searchtree lo hi s), ~ E.lt y x.
Lemma Klt_strictorder: StrictOrder K.lt.
Lemma elements'_spec2 : forall s, valid s -> Sorted.sort E.lt (elements' s nil).