PROOF:

We try to prove by simplification:

[Graphics:submitted.nbgr278.gif] [Graphics:submitted.nbgr279.gif]

Now we prove the formula

[Graphics:submitted.nbgr280.gif] [Graphics:submitted.nbgr281.gif]

by induction on [Graphics:submitted.nbgr282.gif].

Induction base for [Graphics:submitted.nbgr283.gif]:

[Graphics:submitted.nbgr290.gif] [Graphics:submitted.nbgr291.gif]

Induction hypothesis for [Graphics:submitted.nbgr292.gif]:

[Graphics:submitted.nbgr293.gif] [Graphics:submitted.nbgr294.gif].

Induction step for [Graphics:submitted.nbgr295.gif]:

[Graphics:submitted.nbgr304.gif] [Graphics:submitted.nbgr305.gif]