Definition wellFormedFormula : nat -> nat :=
  evalStrongRec 0
    (fun f recs : nat =>
     switchPR (cPairPi1 f)
       (switchPR (pred (cPairPi1 f))
          (switchPR (pred (pred (cPairPi1 f)))
             (switchPR (pred (pred (pred (cPairPi1 f))))
                (charFunction 2 beq_nat
                   (codeArityR (pred (pred (pred (pred (cPairPi1 f))))))
                   (S (codeLength (cPairPi2 f))) *
                 wellFormedTerms (cPairPi2 f))
                (codeNth (f - S (cPairPi2 (cPairPi2 f))) recs))
             (codeNth (f - S (cPairPi2 f)) recs))
          (codeNth (f - S (cPairPi1 (cPairPi2 f))) recs *
           codeNth (f - S (cPairPi2 (cPairPi2 f))) recs))
       (wellFormedTerm (cPairPi1 (cPairPi2 f)) *
        wellFormedTerm (cPairPi2 (cPairPi2 f)))).

Lemma wellFormedFormulaCorrect2 : forall n : nat, wellFormedFormula n <> 0 -> exists f : Formula, codeFormula L codeF codeR f = n.