induction n; intuition; simpl in *.
rewrite app_length.
repeat rewrite map_length.
rewrite plus_0_r.
rewrite <- IHn.
trivial.
Qed.
Fixpoint tailOpt(A : Set)(n : nat)(v : Vector.t A n) : option (Vector.t A (pred n)):=
match v with
| [] => None
| Vector.cons _ _ _ v => Some v
end.

Lemma tailOpt_eq : forall (A : Set)(n : nat)(v1 v2 : Vector.t A n),
v1 = v2 ->
tailOpt v1 = tailOpt v2.