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

Theorem maxDivSimplInvAux :
forall (v : Z) (p q : nat),
p = maxDiv v (S p) -> p = maxDiv v (S (q + p)).