\|} ~{\|g-z\|}_0^0 \nonumber \\ &\leq \min_{g\in \partial\|\beta^\star\|} \,\max_{z\in {\mathcal{B}}^\star} ~{\|g-z\|}_0^0 \nonumber \\ &= \min_{g\in \partial\|\beta^\star\|} \,\max_{z\in {\mathcal{B}}^\star} ~{\|g+z\|}_0^0 \nonumber \\ &\leq \min_{g\in \partial\|\beta^\star\|} \,