Definition checkPrfEQ4 (p recs : nat) :=
let r := cPairPi2 (cPairPi2 p) in
let A := cPair (S (S (S (S r)))) (codeNVars1 (pred (codeArityR r))) in
let B := cPair (S (S (S (S r)))) (codeNVars2 (pred (codeArityR r))) in
notZero (codeArityR r) *
charFunction 2 beq_nat (codeAxmEqHelp (pred (codeArityR r)) (codeIff A B))
(cPairPi1 p).

Lemma checkPrfEQ5IsPR : isPR 2 checkPrfEQ5.
Definition checkPrfHelp : nat -> nat :=
evalStrongRec 0
(fun p recs : nat =>
let type := cPairPi1 (cPairPi2 p) in
switchPR type
(switchPR (pred type)
(switchPR (pred (pred type))
(switchPR (pred (pred (pred type)))
(switchPR (pred (pred (pred (pred type))))
(switchPR (pred (pred (pred (pred (pred type)))))
(switchPR
(pred (pred (pred (pred (pred (pred type))))))
(switchPR
(pred
(pred (pred (pred (pred (pred (pred type)))))))
(switchPR
(pred
(pred
(pred
(pred
(pred (pred (pred (pred type))))))))
(switchPR
(pred
(pred
(pred
(pred
(pred
(pred
(pred (pred (pred type)))))))))
(switchPR
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred (pred (pred type))))))))))
(switchPR
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred (pred (pred type)))))))))))
(switchPR
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred (pred (pred type))))))))))))
(switchPR
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred
(pred (pred (pred type)))))))))))))
0 (checkPrfEQ5 p recs))
(checkPrfEQ4 p recs))
(checkPrfEQ3 p recs))
(checkPrfEQ2 p recs))
(checkPrfEQ1 p recs))
(checkPrfFA3 p recs))
(checkPrfFA2 p recs)) (checkPrfFA1 p recs))
(checkPrfCP p recs)) (checkPrfIMP2 p recs))
(checkPrfIMP1 p recs)) (checkPrfGEN p recs))
(checkPrfMP p recs)) (checkPrfAXM p recs)).