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.

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