induction v.
intros.
inversion H.
intros.
inversion_clear H.
exists (nb0 n).
simpl...
destruct (IHv H0).
exists (Snb x).
rewrite nth_S...
Qed.

Lemma nb_val_eq_rec_r (k u: nat) (n: natBelow u) (h: k = u):
nb_val (eq_rec_r natBelow n h) = nb_val n.