Definition checkPrfGEN (p recs : nat) :=
  switchPR
    (charFunction 2 beq_nat
       (cPair 3
          (cPair (cPairPi1 (cPairPi2 (cPairPi2 p)))
             (cPairPi1 (cPairPi2 (cPairPi2 (cPairPi2 p)))))) 
       (cPairPi1 p) *
     (codeNth (p - S (cPairPi2 (cPairPi2 (cPairPi2 p)))) recs *
      (1 -
       codeIn (cPairPi1 (cPairPi2 (cPairPi2 p)))
         (codeFreeVarListFormula
            (pred (codeNth (p - S (cPairPi2 (cPairPi2 (cPairPi2 p)))) recs))))))
    (codeNth (p - S (cPairPi2 (cPairPi2 (cPairPi2 p)))) recs) 0.

Lemma checkPrfGENIsPR : isPR 2 checkPrfGEN.