User blog comment:Nayuta Ito/faketest/e0/@comment-30754445-20180805015451/@comment-35470197-20180807044129

> Just because the cofinality of the ordinals inside the ψ are different, does not necessarily mean that the final collapsed countable ordinal is different.

I know. I meant that I could not prove \(\psi_{\Omega_1}(\varepsilon_{M+1}) = \psi_{\Omega_1}(\psi_{\chi_{\varepsilon_{M+1}}(0)}(0))\) by the obstruction of the cofinality.