(* Copyright 2012-2015 by Adam Petcher.				* * Use of this source code is governed by the license described	* * in the LICENSE file at the root of the source tree.		*)
Set Implicit Arguments.
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.
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.

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.