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.