Definition codeSysPrfNot :=
existH 2
(andH (substituteFormula LNN codeSysPrf 0 (var 2))
(substituteFormula LNN
(substituteFormula LNN (primRecFormula 1 (proj1_sig codeNotIsPR)) 0
(var 2)) 1 (var 0))).

Lemma codeSysPrfNCorrect2 :
forall (f : fol.Formula L) (A : fol.Formulas L),
(exists g : fol.Formula L, In g A /\ ~ mem _ U g) ->
forall p : Prf L A (fol.notH L f),
SysPrf T
(notH
(substituteFormula LNN
(substituteFormula LNN codeSysPrfNot 0
(natToTerm (codeFormula L codeF codeR f))) 1
(natToTerm (codePrf L codeF codeR A (fol.notH L f) p)))).