Equation 22.1.872B233D0F0F88

\begin{equation} A^{\mathrm{An}}(v)\coloneqq \sup _{\tau \leq \tau _0} (A_\tau ^{\mathrm{An}}(v)+\tau )=\max _{i=0,\ldots ,N} \left(A_{\tau _ i}^{\mathrm{An}}(v)+\tau _ i\right)\quad \forall v\in X^{\mathrm{An}}. \end{equation}