Definition inlist {A: Type}{EA: EqDec A} (x: A) (vl: list A) : bool :=
   existsb (fun y => if eq_dec x y then true else false) vl.

(* Specifications: *)
Lemma inlist_notIn {A: Type}{EA: EqDec A}: forall (x: A) (vl: list A), inlist x vl = false -> ~ In x vl.