intros v p q H' H'0.
replace q with (S (q - S p + p)); auto with zarith.
apply maxDivSimplInvAux; auto.
Qed.

(* Specifications: *)
Theorem maxDivUnique :
forall (v : Z) (p : nat),
p = maxDiv v (S p) ->
Zdivides v (Zpower_nat radix p) /\ ~ Zdivides v (Zpower_nat radix (S p)).