Definition checkPrfFA3 (p recs : nat) :=
  let A := cPairPi1 (cPairPi2 (cPairPi2 p)) in
  let B := cPairPi1 (cPairPi2 (cPairPi2 (cPairPi2 p))) in
  let v := cPairPi2 (cPairPi2 (cPairPi2 (cPairPi2 p))) in
  charFunction 2 beq_nat
    (cPair 1
       (cPair (cPair 3 (cPair v (cPair 1 (cPair A B))))
          (cPair 1 (cPair (cPair 3 (cPair v A)) (cPair 3 (cPair v B))))))
    (cPairPi1 p).

Lemma checkPrfFA3IsPR : isPR 2 checkPrfFA3.