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 reduceAddForalls :
forall (n m : nat) (A B : Formula),
SysPrf NN (iffH A B) ->
SysPrf NN (iffH (addForalls m n A) (addForalls m n B)).