Module Import P := Properties M.
Hint Resolve elements_spec2 : core.
Hint Immediate
min_elt_spec1 min_elt_spec2 min_elt_spec3
max_elt_spec1 max_elt_spec2 max_elt_spec3 : set.
Definition gtb x y := match E.compare x y with Gt => true | _ => false end.
Definition leb x := fun y => negb (gtb x y).
Definition elements_lt x s := List.filter (gtb x) (elements s).
Definition elements_ge x s := List.filter (leb x) (elements s).

Lemma leb_1 : forall x y, leb x y = true <-> ~E.lt y x.