Proof using.
intros.
rewrite <- app_ass in *.
find_apply_lem_hyp NoDup_remove.
rewrite app_ass in *.
intuition.
Qed.

Lemma NoDup_app3_not_in_2 :
forall (xs ys zs : list A) b,
NoDup (xs ++ ys ++ b :: zs) ->
In b ys ->
False.