induction n; intuition.
omega.
destruct (vector_S v).
destruct H0.
exists (Vector.cons bool (negb x) n x0).
intuition.
rewrite H0 in H1.
inversion H1.
destruct x; simpl in *; discriminate.
Qed.

Lemma map_eq_inv :
forall (A B : Set)(f1 f2 : A -> B)(ls : list A),
map f1 ls = map f2 ls ->
forall a, In a ls -> f1 a = f2 a.