Definition ReplaceFormulaTerm : nat -> nat -> nat :=
  evalStrongRec 1
    (fun f recs s : nat =>
     switchPR (cPairPi1 f)
       (switchPR (pred (cPairPi1 f))
          (switchPR (pred (pred (cPairPi1 f)))
             (switchPR (pred (pred (pred (cPairPi1 f))))
                (cPair (cPairPi1 f) (ReplaceTermsTerm (cPairPi2 f) s))
                (cPair 3
                   (cPair s (codeNth (f - S (cPairPi2 (cPairPi2 f))) recs))))
             (cPair 2 (codeNth (f - S (cPairPi2 f)) recs)))
          (cPair 1
             (cPair (codeNth (f - S (cPairPi1 (cPairPi2 f))) recs)
                (codeNth (f - S (cPairPi2 (cPairPi2 f))) recs))))
       (cPair 0
          (cPair (ReplaceTermTerm (cPairPi1 (cPairPi2 f)) s)
             (ReplaceTermTerm (cPairPi2 (cPairPi2 f)) s)))).

Lemma ReplaceFormulaTermMonotone : forall a s1 s2 : nat, s1 <= s2 -> ReplaceFormulaTerm a s1 <= ReplaceFormulaTerm a s2.