induction n; intuition; simpl in *.
intuition.
apply in_app_or in H.
simpl in *.
intuition.
Qed.

Lemma app_NoDup : forall(A : Set)(ls1 ls2 : list A),
NoDup ls1 ->
NoDup ls2 ->
(forall a, In a ls1 -> ~In a ls2) ->
(forall a, In a ls2 -> ~In a ls1) ->
NoDup (ls1 ++ ls2).