Definition checkPrfEQ4 (p recs : nat) :=
  let r := cPairPi2 (cPairPi2 p) in
  let A := cPair (S (S (S (S r)))) (codeNVars1 (pred (codeArityR r))) in
  let B := cPair (S (S (S (S r)))) (codeNVars2 (pred (codeArityR r))) in
  notZero (codeArityR r) *
  charFunction 2 beq_nat (codeAxmEqHelp (pred (codeArityR r)) (codeIff A B))
    (cPairPi1 p).

Lemma codeIffIsPR : isPR 2 codeIff.