Proof using.
intros l l' a H_pm.
assert (In a (a :: l)); auto with datatypes.
assert (In a l'); eauto using Permutation_in.
find_apply_lem_hyp In_split; auto.
Qed.

(* Specifications: *)
Lemma NoDup_app_left :
forall (l l' : list A),
NoDup (l ++ l') -> NoDup l.