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)).

Lemma checkPrfHelpIsPR : isPR 1 checkPrfHelp.