Fixpoint contains (L H: Z) (s: t) : bool :=
match s with
| Nil => false
| Cons l h s' => (zle H h && zle l L) || contains L H s'
end.

(* Specifications: *)
Lemma contains_In:
forall l0 h0, l0 < h0 -> forall s, ok s ->
(contains l0 h0 s = true <-> (forall x, l0 <= x < h0 -> In x s)).
Lemma contains_In:
forall l0 h0, l0 < h0 -> forall s, ok s ->
(contains l0 h0 s = true <-> (forall x, l0 <= x < h0 -> In x s)).