Definition checkPrfEQ1 (p recs : nat) :=
  charFunction 2 beq_nat (cPairPi2 (cPairPi2 p)) 0 *
  charFunction 2 beq_nat
    (codeFormula L codeF codeR (fol.equal L (fol.var L 0) (fol.var L 0)))
    (cPairPi1 p).

Lemma checkPrfEQnIsPR : forall n : nat, isPR 2 (fun p recs : nat => charFunction 2 beq_nat (cPairPi2 (cPairPi2 p)) 0 * charFunction 2 beq_nat n (cPairPi1 p)).