 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 $$0=u(t_0,x_0)-\varphi(t_0,x_0)=\underset{(t,x)\in[0,T)\times \R^d}{\min}(u-\varphi)(t,x).$$ 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} \nonumber\varphi(t_0,x_0)=u(t_0,x_0) &= \underset{\mathbb P\in\mathcal P^{t_0,\kappa}_h}{\sup} \mathcal Y^{\mathbb P,t_0,x_0}_{t_0}\left(t_0+\eta,u(t_0+\eta,B_{t_0+\eta}^{t_0,x_0})\right)\\ &\