Definition subStar (a v n : nat) := codeSubFormula a v (codeNatToTerm n).

(* Specifications: *)
Lemma subStarIsPR : isPR 3 subStar.
Lemma FixPointLNN : forall (A : Formula) (v : nat), {B : Formula | SysPrf NN (iffH B (substituteFormula LNN A v (natToTermLNN (codeFormula B)))) /\ (forall x : nat, In x (freeVarFormula LNN B) <-> In x (list_remove _ eq_nat_dec v (freeVarFormula LNN A)))}.
Lemma FixPointLNT : forall (A : Formula) (v : nat), {B : Formula | SysPrf PA (iffH B (substituteFormula LNT A v (natToTermLNT (codeFormula B)))) /\ (forall x : nat, In x (freeVarFormula LNT B) <-> In x (list_remove _ eq_nat_dec v (freeVarFormula LNT A)))}.