Fixpoint forNats(n : nat) :=
  match n with
      | 0 => nil
      | S n' =>
        cons n' (forNats n')
  end.

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