induction n; destruct ls; intuition; simpl in *.
inversion H; clear H; subst.
simpl.
trivial.
inversion H; clear H; subst.
simpl.
trivial.
discriminate.
case_eq (shiftOut ls n); intuition.
rewrite H0 in H.
destruct p.
inversion H; clear H; subst.
simpl.
f_equal.
apply IHn in H0.
subst.
trivial.
rewrite H0 in H.
discriminate.
Qed.

Lemma to_list_length : forall (A : Set)(m : nat)(v : Vector.t A m),
length (Vector.to_list v) = m.