revert n x y.
apply (double_rect (fun n (x y: Vector.t A n) => ext_eq (nth x) (nth y) -> x = y))...
intros.
cset (H0 (nb0 n)).
simpl in H1.
subst.
rewrite H...
intro.
cset (H0 (Snb x)).
repeat rewrite nth_S in H1...
Qed.

(* Specifications: *)
Lemma In_nth A n i (v: Vector.t A n): List.In (nth v i) v.
Proof with auto.