User blog comment:P進大好きbot/Please Help me on study of Pair Sequence System (2-rowed Bashicu Matrix System)/@comment-35392788-20180813124110/@comment-106.181.212.42-20180813220031

@Syst3ms

>I think there is something else wrong. Have you checked if the lemmas apply provided specific criteria ?

Yes. I have checked. Lemma 1.2 always holds. What is wrong?

@De

> So Buchholz function doesn't grow between \psi_0(\psi_1(\psi_2(0))) and \psi_0(\psi_2(0)). Hence \psi_0(\psi_1(\psi_2(0)))=\psi_0(\psi_2(0))

I know it. It is a special equality only for \(\psi_2\). What I am arguing with is the inequality \begin{eqnarray*} \psi_0(\psi_1(\psi_2(\psi_3(0)))) < \psi_0(\psi_3(0)), \end{eqnarray*} which is assumed to be an equality in many analyses. This is one reason why I asked these questions.