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 checkPrfHelpIsPR : isPR 1 checkPrfHelp.
set
(f :=
list_rec (fun _ => nat -> nat -> nat -> nat) (fun _ _ _ : nat => 0)
(fun (a : nat -> nat -> nat) (l : list (nat -> nat -> nat))
(rec : nat -> nat -> nat -> nat) (n p recs : nat) =>
switchPR (iterate pred n (cPairPi1 (cPairPi2 p)))
(rec (S n) p recs) (a p recs))) in *.