(** * [mem] *)

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.

(* Specifications: *)
Lemma mem_1 : forall m (Hm:NoDupA m) x, In x m -> mem x m = true.
Lemma mem_2 : forall m (Hm:NoDupA m) x, mem x m = true -> In x m.