Consider $(\mathcal{M},g_{\beta})$ with sufficiently large gluing parameter $\beta\gg 1$. Let $\delta$, $\nu$ and $\mu$ be the constants in Proposition 9.2, then there are constants $r_{0}>0$ and $C>0$ which are independent $\beta$, such that for every $\bm{v}_{1}\equiv(\bm{\eta}_{1},\bar{\bm{\xi}}_{1}^{+})\in B_{r}(0)\subset\mathfrak{A}$ and $\bm{v}_{2}\equiv(\bm{\eta}_{2},\bar{\bm{\xi}}_{2}^{+})\in B_{r}(0)\subset\mathfrak{A}$, where $r<r_{0}$, we have