(** * [is_empty] *)

(* Specifications: *)
Lemma is_empty_1 :forall m, Empty m -> is_empty m = true.
Lemma is_empty_2 : forall m, is_empty m = true -> Empty m.
Fixpoint mem (k : key) (s : t elt) {struct s} : bool :=
match s with
| nil => false
| (k',_) :: l => if X.eq_dec k k' then true else mem k l
end.
Lemma is_empty_1 :forall m, Empty m -> is_empty m = true.
Lemma is_empty_2 : forall m, is_empty m = true -> Empty m.
Fixpoint mem (k : key) (s : t elt) {struct s} : bool :=
match s with
| nil => false
| (k',_) :: l =>
match X.compare k k' with
| LT _ => false
| EQ _ => true
| GT _ => mem k l
end
end.