induction 1; intuition; simpl in *.
eapply Permutation_app.
eapply Permutation_refl.
trivial.
repeat rewrite app_assoc.
eapply Permutation_app.
eapply Permutation_app_comm.
eapply Permutation_refl.
eapply perm_trans.
eapply IHPermutation1.
trivial.
Qed.

Lemma to_list_nil_inv : forall (A : Type)(n : nat)(v : Vector.t A n),
Vector.to_list v = nil ->
n = O.