Proof using.
induction l; intros; simpl in *.
- apply NoDup_nil.
- invc_NoDup.
find_apply_hyp_hyp.
apply NoDup_cons; auto.
intro.
match goal with H: ~ In _ _ |- _ => contradict H end.
apply in_or_app.
left; auto.
Qed.

Lemma NoDup_app_right :
forall (l l' : list A),
NoDup (l ++ l') -> NoDup l'.