Proof with auto.
revert f.
induction v...
intros.
simpl.
apply (IHv (fun (m: nat) (w: Vector.t X m) => f (S m) (Vector.cons h w))).
Qed.

Lemma eq_as_lists X n (x y: Vector.t X n): to_list x = to_list y -> x = y.
Proof with auto.