induction n1; intuition; simpl in *.
destruct (vector_S x).
destruct H.
subst.
simpl.
remember (splitVector n1 n2 x1) as z.
destruct z.
simpl.
f_equal.
specialize (IHn1 n2 x1).
rewrite <- Heqz in IHn1.
simpl in *.
trivial.
Qed.

Theorem append_splitVector:
forall (A : Set) n1 n2 (x : Vector.t A (n1 + n2)) x1 x2,
(x1, x2) = (splitVector n1 n2 x) ->
(Vector.append x1 x2) = x.