Fixpoint RepresentableHelp (n : nat) : naryFunc n -> Formula -> Prop :=
  match n return (naryFunc n -> Formula -> Prop) with
  | O =>
      fun (f : naryFunc 0) (A : Formula) =>
      SysPrf T (iffH A (equal (var 0) (natToTerm f)))
  | S m =>
      fun (f : naryFunc (S m)) (A : Formula) =>
      forall a : nat,
      RepresentableHelp m (f a) (substituteFormula LNN A (S m) (natToTerm a))
  end.

(* Specifications: *)
Lemma RepresentableHalfHelp : forall (n : nat) (f : naryFunc n) (A : Formula), RepresentableHalf1 n f A -> RepresentableHalf2 n f A -> RepresentableHelp n f A.