Proof with auto.
induction v...
simpl.
rewrite IHv.
rewrite (e h)...
Qed. (* todo: as a morphism *)

Lemma natBelow_S_inv' (n: nat) (P: natBelow (S n) -> Type):
P (nb0 n) -> (forall m, P (Snb m)) -> forall x, P x.