(*The wellFormedness requirement isn't really neccesary,
because and proof that used ``extra symbols'' could be
turned into a proof that only used symbols from the
axioms and the conclusion.

However making this assumption makes the proof easier *)

(* p is (cPair (formula) (proof of the Formula)) *)

Definition checkPrfAXM (p recs : nat) :=
  switchPR (charFunction 2 beq_nat (cPairPi2 (cPairPi2 p)) (cPairPi1 p))
    (S (S (cPair (cPairPi1 p) 0))) 0.

Lemma checkPrfAXMIsPR : isPR 2 checkPrfAXM.