Module ME := OrderedTypeFacts E.
Definition empty : t := let (s, _) := empty in s.
Definition is_empty (s : t) : bool :=
if is_empty s then true else false.
Definition mem (x : elt) (s : t) : bool :=
if mem x s then true else false.

Lemma mem_1 : forall (s : t) (x : elt), In x s -> mem x s = true.