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 codeInductionSchemaIsPR : isPRrel 1 codeInductionSchema.
Definition codePA : nat -> bool :=
orRel 1 (beq_nat (codeFormula PA6))
(orRel 1 (beq_nat (codeFormula PA5))
(orRel 1 (beq_nat (codeFormula PA4))
(orRel 1 (beq_nat (codeFormula PA3))
(orRel 1 (beq_nat (codeFormula PA2))
(orRel 1 (beq_nat (codeFormula PA1)) codeInductionSchema))))).