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

(* 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).