Definition checkPrfFA2 (p recs : nat) :=
  let A := cPairPi1 (cPairPi2 (cPairPi2 p)) in
  let v := cPairPi2 (cPairPi2 (cPairPi2 p)) in
  (1 - codeIn v (codeFreeVarFormula A)) *
  charFunction 2 beq_nat (cPair 1 (cPair A (cPair 3 (cPair v A))))
    (cPairPi1 p).

Lemma checkPrfFA2IsPR : isPR 2 checkPrfFA2.