Section Code_PA.
Let codeTerm := codeTerm LNT codeLNTFunction.
Let codeFormula := codeFormula LNT codeLNTFunction codeLNTRelation.
Let codeFormulaInj :=
codeFormulaInj LNT codeLNTFunction codeLNTRelation codeLNTFunctionInj
codeLNTRelationInj.
Definition codeOpen : nat -> nat :=
evalStrongRec 0
(fun f recs : nat =>
switchPR (cPairPi1 f)
(switchPR (pred (cPairPi1 f))
(switchPR (pred (pred (cPairPi1 f)))
(switchPR (pred (pred (pred (cPairPi1 f)))) f
(codeNth (f - S (cPairPi2 (cPairPi2 f))) recs)) f) f) f).

Lemma codePAcorrect2 :
forall f : Formula,
~ mem Formula PA f -> codePA (codeFormula f) = false.