\begin{frame}{Regular Expressions $\iff$ Regular Languages}
\begin{block}{Theorem}
A language $L$ is \emph{regular} \\
\hfill $\iff$ there is a \emph{regular expression} $r$ with $L(r) = L$.
\end{block}
\pause\medskip
\begin{proof}
We need to prove two directions:
\begin{itemize}
\medskip
\item $(\Leftarrow)$
Translate regular expressions into NFAs.
\medskip
\item $(\Rightarrow)$
Translate NFAs into regular expressions.
\medskip
\end{itemize}
\end{proof}
\end{frame}