 there exists $\xi<\kappa$ such that for all $\xi<\alpha<\kappa$, there exists $\gamma_0\in \xi_{b(\alpha,0)+0}\setminus\xi_{b(\alpha,0)}$ and $\gamma_0\in \xi_{b(\alpha,0)+0}\setminus\xi_{b(\alpha,0)}$ such that $a(\gamma_0)\neq z(\gamma_0)$ and $a(\gamma_0)\neq z(\gamma_0)$,  (