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

Lemma freeVarAddExists2 : forall (n m v : nat) (A : Formula), In v (freeVarFormula LNN (addExists m n A)) -> n + m <= v \/ v < m.