Definition min_elt: t -> option elt := choose.

(* Specifications: *)
Lemma elements_spec2 : forall s, Sorted.sort E.lt (elements s).
Lemma elements_spec2w : forall s, SetoidList.NoDupA E.eq (elements s).
Lemma min_elt_spec1
: forall (s : t) (x : elt), min_elt s = Some x -> In x s.
Lemma min_elt_spec3 : forall s, min_elt s = None -> Empty s.
Lemma max_elt_spec1 : forall s x, max_elt s = Some x -> In x s.
Lemma max_elt_spec2 : forall s x y, max_elt s = Some x -> In y s -> ~ E.lt x y.
Lemma max_elt_spec3 : forall s, max_elt s = None -> Empty s.
Lemma choose_spec3 : forall s s' x y,
choose s = Some x -> choose s' = Some y ->
Equal s s' -> E.eq x y.