Proof using.
intros l m H'; elim H'; simpl in |- *; auto.
intros l1 l2 l3 H'0 H'1 H'2 H'3.
rewrite <- H'3; auto.
Qed.

(* Specifications: *)
(* A permutation of the nil list is the nil list *)
Theorem permutation_nil_inv : forall l : list A, permutation l nil -> l = nil.
Proof using.