\begin{frame}{Decidability of Equivalence} \begin{goal}{Theorem} It is decidable if two regular languages $L_1$ and $L_2$ are equal. \end{goal} \pause \begin{proof} We have \begin{talign} L_1 = L_2 \quad\iff\quad \mpause[1]{ (L_1 \subseteq L_2) \wedge (L_2 \subseteq L_1) } \end{talign} \pause\pause Both problems on the right are decidable. \end{proof} \end{frame}