(* ********************************************************************** *)
(** * List non-membership *)

(* Specifications: *)
Lemma not_In_cons : forall (A : Type) (ys : list A) (x y : A),
x <> y ->
~ In x ys ->
~ In x (y :: ys).
Lemma InA_iff_In : forall (A : Type) (x : A) (xs : list A),
InA (@eq _) x xs <-> In x xs.