intros v p H'; split.
rewrite H'.
apply maxDivCorrect; auto.
red in |- *; intros H'0; generalize H'; clear H'.
simpl in |- *.
case (ZdividesP v (radix * Zpower_nat radix p)); simpl in |- *; auto.
intros H' H'1; Contradict H'1; auto with zarith.
Qed.

Theorem maxDivUniqueDigit :
forall v : Z,
v <> 0 ->
Zdivides v (Zpower_nat radix (maxDiv v (digit radix v))) /\
~ Zdivides v (Zpower_nat radix (S (maxDiv v (digit radix v)))).