Fixpoint addForalls (m n : nat) (f : Formula) {struct n} : Formula :=
match n with
| O => f
| S n' => forallH (n' + m) (addForalls m n' f)
end.

Lemma freeVarAddForalls2 :
forall (n m v : nat) (A : Formula),
In v (freeVarFormula LNN (addForalls m n A)) -> n + m <= v \/ v < m.