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 freeVarAddForalls1 : forall (n m v : nat) (A : Formula), In v (freeVarFormula LNN (addForalls m n A)) -> In v (freeVarFormula LNN A).