Definition checkPrfMP (p recs : nat) :=
  switchPR
    (wellFormedFormula (cPairPi1 (cPairPi2 (cPairPi2 (cPairPi2 p)))) *
     (charFunction 2 beq_nat (cPairPi1 (cPairPi1 (cPairPi2 (cPairPi2 p))))
        (codeImp (cPairPi1 (cPairPi2 (cPairPi2 (cPairPi2 p)))) (cPairPi1 p)) *
      (codeNth (p - S (cPairPi1 (cPairPi2 (cPairPi2 p)))) recs *
       codeNth (p - S (cPairPi2 (cPairPi2 (cPairPi2 p)))) recs)))
    (S
       (codeApp
          (pred (codeNth (p - S (cPairPi1 (cPairPi2 (cPairPi2 p)))) recs))
          (pred (codeNth (p - S (cPairPi2 (cPairPi2 (cPairPi2 p)))) recs))))
    0.

Lemma checkPrfMPIsPR : isPR 2 checkPrfMP.