Proof using.
induction l; intros; simpl in *; auto.
invc_NoDup.
find_apply_hyp_hyp; auto.
Qed.

(* Specifications: *)
Lemma NoDup_in_not_in_right :
forall (l l' : list A) (a : A),
NoDup (l ++ l') -> In a l -> ~ In a l'.