 $$\begin{aligned} \Pr_{x^{\mu}}\left[\sum_{i\in[n]}a_{i}x^{\mu}_{i}=c_{0}\right] & \geq & \Pr_{(x^{\mu}_{i})_{i\in U_{0}}}\left[\sum_{i\in U_{0}}a_{i}x^{\mu}_{i}=c_{0}\right]\prod_{j\in U_{0}}\Pr_{x^{\mu}_{j}}\left[x^{\mu}_{j}=0\right]\\  & \geq & \rho^{\ring}_{\mu}\left(a|_{U_{0}}\right)\