#[global]
  Instance gtb_compat x : Proper (E.eq==>Logic.eq) (gtb x).#[global]
  Instance leb_compat x : Proper (E.eq==>Logic.eq) (leb x).

(* Specifications: *)
Lemma elements_split : forall x s, elements s = elements_lt x s ++ elements_ge x s.
Lemma elements_Add : forall s s' x, ~In x s -> Add x s s' -> eqlistA E.eq (elements s') (elements_lt x s ++ x :: elements_ge x s).