\begin{align}\label{realtt1}
    &\alpha  \mathrm{\bold{D}}_2(\mu,\mu^*)+\vartheta P_{2,H}\big(\varrho(\bar{\beta}-\bar{\beta}^*)_{\mathcal{J}^*};\lambda\big)+\|\varrho(\bar{\beta}-\bar{\beta}^*)_{\mathcal{J}^*}\|_{2,P(\cdot;\lambda)}\nonumber\\\leq&\,  \bold{\Delta}_{l}(\mu,\mu^*)+\|\varrho(\bar{\beta}-\bar{\beta}^*)_{\mathcal{J}^{*C}}\|_{2,P(\cdot;\lambda)}-\vartheta P_{2,H}\big(\varrho(\bar{\beta}-\bar{\beta}^*)_{\mathcal{J}^{*C}};\lambda\big)+K\lambda^2J^*.
\end{align}
