&\leq \underset{\P\in\Pc^\kappa_h}{\sup}\E^\P\left[{\left|\mathfrak y_t^\P(t,x)-\mathfrak y_{t'}^\P(t',x) \right|}\right]\\ &\leq \underset{\P\in\Pc^\kappa_h}{\sup}\E^\P\left[{\left|\mathfrak y_t^\P(t,x)-\mathfrak y_{t}^\P(t',x) \right|}\right]