intros n0; apply digitInv; auto.
rewrite Zabs_eq.
cut (Zpower_nat n (pred (S n0)) < Zpower_nat n (S n0))%Z; auto with zarith.
cut (0 < Zpower_nat n (S n0))%Z; auto with zarith.
rewrite Zabs_eq; auto with zarith.
Qed.

Theorem digit_bound :
forall (x y z : Z) (n : nat),
(Zabs x <= Zabs y)%Z ->
(Zabs y <= Zabs z)%Z -> digit x = n -> digit z = n -> digit y = n.