 super-solution property. Let $\varphi\in C^{0}_b([0,T)\times\R^d)$ and $(t_0,x_0)\in[0,T)\times\R^d$ be such that $$0=u(t_0,x_0)-\varphi(t_0,x_0)=\underset{(t,x)\in[0,T)\times \R^d}{\max}(u-\varphi)(t,x).$$ Fix some $\eta>0$ such that $t_0+\eta<T$. By with the constant family of stopping times $t_0+\eta$, we know that $$\begin{aligned} \label{ineq:visco