intuition.
destruct v; simpl in *.
trivial.
unfold Vector.to_list in *.
discriminate.
Qed.

Lemma app_second_eq :
forall (A : Type) (ls2 ls1 ls3 : list A),
ls1 = ls2 ++ ls3 -> length ls1 = length ls3 -> ls1 = ls3 /\ ls2 = nil.