intros v p H' H'0; simpl in |- *.
case (ZdividesP v (radix * Zpower_nat radix p)); auto.
intros H'1; case H'0; simpl in |- *; auto.
intros H'1.
generalize H'; case p; simpl in |- *; auto.
intros n H'2; case (ZdividesP v (radix * Zpower_nat radix n)); auto.
intros H'3; case H'3; auto.
Qed.

Theorem maxDivUniqueInverseDigit :
forall (v : Z) (p : nat),
v <> 0 ->
Zdivides v (Zpower_nat radix p) ->
~ Zdivides v (Zpower_nat radix (S p)) -> p = maxDiv v (digit radix v).