Fixpoint splitVector(A : Set)(n m : nat) : Vector.t A (n + m) -> (Vector.t A n * Vector.t A m) :=
  match n with
          | 0 => 
            fun (v : Vector.t A (O + m)) => (@Vector.nil A, v)
          | S n' => 
            fun (v : Vector.t A (S n' + m)) => 
              let (v1, v2) := splitVector _ _ (Vector.tl v) in
                (Vector.cons _ (Vector.hd v) _ v1, v2)
    end.

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.