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-35470197-20180813143856

> The third inequality is wrong. ψ 0 (ψ 1 (ψ 3 (0)))>ψ 0 (ψ 2 (0)) ψ0(ψ1(ψ3(0)))>ψ0(ψ2(0))

Lemma 1.2 (a) and (c) in [Buc]: \(\psi_1(\psi_3(0)) < \Omega_2 = \psi_2(0)\)

Lemma 1.2 (d) in [Buc]: \(\alpha \leq \beta\) implies \(\psi_0(\alpha) \leq \psi_0(\beta)\)

Therefore we have \(\psi_0(\psi_1(\psi_3(0))) \leq \psi_0(\psi_2(0))\).

What is wrong here?