Let primRecSigmaFormula (n : nat) (SigA SigB : Formula) : Formula :=
existH (S (S n))
(andH
(minimize (primRecSigmaFormulaHelp n SigA SigB)
(primRecPiFormulaHelp n SigA SigB) (S (S n))
(S (S (S (S n)))))
(substituteFormula LNN
(substituteFormula LNN betaFormula 2 (var (S (S n)))) 1
(var (S n)))).
Remark notBoundedForall :
forall (P : nat -> Prop) (b : nat),
(forall x : nat, decidable (P x)) ->
~ (forall n : nat, n < b -> P n) -> exists n : nat, n < b /\ ~ P n.

(* Specifications: *)
Lemma succ_plus_discr : forall n m : nat, n <> S (m + n).
Lemma n_SSn : forall n : nat, n <> S (S n).
Lemma n_SSSn : forall n : nat, n <> S (S (S n)).
Lemma n_SSSSn : forall n : nat, n <> S (S (S (S n))).
Remark In_betaFormula_subst_1_2_0 :
forall (a b c : Term) (v : nat),
In v
(freeVarFormula LNN
(substituteFormula LNN
(substituteFormula LNN (substituteFormula LNN betaFormula 1 a) 2 b)
0 c)) ->
In v (freeVarTerm LNN a) \/
In v (freeVarTerm LNN b) \/ In v (freeVarTerm LNN c).