$-bands in ${\Delta}$ and every $a_i$-band $\Gamma$ of ${\Delta}$ is a disk subdiagram of ${\Delta}$ such that $${\partial}|_{(f_0)_-} \Gamma = f_0 s_0 f_0 s_0 ,$$ where $f_0, f_0$ are edges of ${\partial}{\Delta}$ 