intros; subst.
assert (ls3 = nil).
rewrite app_length in H0.
assert (length ls3 = O).
omega.
destruct ls3; simpl in *; try omega; trivial.
subst.
rewrite app_nil_r.
intuition.
Qed.

Lemma to_list_eq_inv : forall (A : Set) n (v1 v2 : Vector.t A n),
VectorDef.to_list v1 = VectorDef.to_list v2 ->
v1 = v2.