intros v p H' H'0 H'1.
apply maxDivSimplInv; auto.
2: apply maxDivUniqueInverse; auto.
apply Zpower_nat_anti_monotone_lt with (n := radix); auto.
apply Zle_lt_trans with (m := Zabs v); auto.
rewrite <- (fun x => Zabs_eq (Zpower_nat radix x)); auto with zarith;
apply ZDividesLe; auto.
apply digitMore; auto.
Qed.

Theorem maxDivPlus :
forall (v : Z) (n : nat),
v <> 0 ->
maxDiv (v * Zpower_nat radix n) (digit radix v + n) =
maxDiv v (digit radix v) + n.