induction v1; intuition; simpl in *.
remember ( splitVector n n2 (Vector.append v1 v2)) as z.
destruct z.
rewrite IHv1 in Heqz.
inversion Heqz; subst.
trivial.
Qed.

(* Specifications: *)
Theorem append_splitVector_h :
forall (A : Set) n1 n2 (x : Vector.t A (n1 + n2)),
(Vector.append (fst (splitVector n1 n2 x)) (snd (splitVector n1 n2 x))) = x.
Theorem append_splitVector_h :
forall (A : Set) n1 n2 (x : Vector.t A (n1 + n2)),
(Vector.append (fst (splitVector n1 n2 x)) (snd (splitVector n1 n2 x))) = x.