induction n; simpl in *; intuition.
destruct s1; simpl in *.
inversion H; clear H; subst.
destruct s2; simpl.
trivial.
trivial.
inversion H; clear H; subst.
rewrite app_comm_cons.
trivial.
destruct s1; simpl in *.
discriminate.
case_eq (shiftOut s1 n); intuition.
rewrite H0 in H.
destruct p.
inversion H; clear H; subst.
erewrite IHn; eauto.
rewrite H0 in H.
discriminate.
Qed.

Lemma shiftOut_lt : forall ls n,
length ls < n ->
shiftOut ls n = None.