\begin{frame}<1-3>[label=development example]
\small
\begin{definition}
\smallskip
A \alert<1>{development} of set of redex positions $Q$ in term $t$ is a rewrite
sequence starting \\ from $t$ in which all contracted redex positions
descend from positions in $Q$.
\end{definition}
\bigskip
\begin{example}
\smallskip
\begin{itemize}
\item
rewrite rules
\vspace{-1ex}
\GREEN{\begin{xalignat*}{2}
\m{0} + y & \to y &
\m{0} \times y &\to \m{0} \\
\m{s}(x) + y &\to \m{s}(x + y) &
\m{s}(x) \times y &\to (x \times y) + y
\end{xalignat*}}
\vspace{-3ex}
\item
rewrite sequences
\vspace{-1ex}
\GREEN{\begin{alignat*}{2}
\underline{\m{s}(\m{0}) \alert{\times} (\m{0} \alert{\times} \m{0})}
&\to (\m{0} \times \underline{(\m{0} \alert{\times} \m{0})}) + (\m{0} \alert{\times} \m{0})
\to (\m{0} \times \m{0}) + (\m{0} \alert{\times} \m{0})
&\qquad&
\only{\alt<5>{\huil}{\lach}}
\only{\lach}
\\
\onslide<2->{\underline{\m{s}(\m{0}) \alert{\times} (\m{0} \alert{\times} \m{0})}}
&\onslide<2->{\to
\underline{(\m{0} \times (\m{0} \alert{\times} \m{0})}) + (\m{0} \alert{\times} \m{0})
\to \m{0} + (\m{0} \alert{\times} \m{0})}
&& \onslide<2->{\huil}
\\
\onslide<3->{\m{s}(\m{0}) \alert{\times} \underline{(\m{0} \alert{\times} \m{0})}}
&\onslide<3->{\to \underline{\m{s}(\m{0}) \alert{\times} \m{0}}
\to (\m{0} \times \m{0}) + \m{0}}
&& \onslide<3->{\lach}
\end{alignat*}}
\vspace{-3ex}
\end{itemize}
\end{example}
\end{frame}