Definition checkPrfCP (p recs : nat) :=
  let A := cPairPi1 (cPairPi2 (cPairPi2 p)) in
  let B := cPairPi2 (cPairPi2 (cPairPi2 p)) in
  charFunction 2 beq_nat
    (cPair 1
       (cPair (cPair 1 (cPair (cPair 2 A) (cPair 2 B))) (cPair 1 (cPair B A))))
    (cPairPi1 p).

Lemma checkPrfCPIsPR : isPR 2 checkPrfCP.