PROOF:

We try to prove by simplification:

[Graphics:submitted.nbgr320.gif] [Graphics:submitted.nbgr321.gif]

Now we prove the formula

[Graphics:submitted.nbgr322.gif] [Graphics:submitted.nbgr323.gif]

by induction on [Graphics:submitted.nbgr324.gif].

Induction base for [Graphics:submitted.nbgr325.gif]:

We prove

[Graphics:submitted.nbgr335.gif] [Graphics:submitted.nbgr336.gif].

Induction hypothesis for [Graphics:submitted.nbgr337.gif]:

[Graphics:submitted.nbgr338.gif] [Graphics:submitted.nbgr339.gif].

Induction step for [Graphics:submitted.nbgr340.gif]:

We prove

[Graphics:submitted.nbgr341.gif] [Graphics:submitted.nbgr342.gif].

For this, we take in [Graphics:submitted.nbgr343.gif] all variables arbitrary but fixed and prove

[Graphics:submitted.nbgr354.gif] [Graphics:submitted.nbgr355.gif]