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)).