\begin{frame}
\small

\begin{definitions}
\smallskip
\begin{itemize}
\item
\makebox[12mm][l]{\alert<.>{$s \subterm t$}}
$s$ is \alert<2>{subterm} of $t$
\begin{itemize}
\item
$s = t$ \onslide<2->or
\smallskip
\item
$t = f(\seq{t})$ and $s \subterm t_i$ for some $1 \leqslant i \leqslant n$
\end{itemize}
\smallskip
\item<3->
\makebox[12mm][l]{\alert<3>{$s \prsubterm t$}}
$s$ is \alert<3>{proper} subterm of $t$
\begin{itemize}
\item
$s \subterm t$ and $s \neq t$
\smallskip
\end{itemize}
\end{itemize}
\end{definitions}

\bigskip

\begin{example}<4->
\smallskip
term \GREEN{$\alert<11>{(\alert<6>{\alert<4>{2}:\alert<5>{x}})+
(\alert<10>{(\alert<8>{\alert<7>{1}:x}):\alert<9>{y}})}$} has subterms
\[
\GREEN{
2 \qquad \onslide<5->
x \qquad \onslide<6->
2:x \qquad \onslide<7->
1 \qquad \onslide<8->
1:x \qquad \onslide<9->
y \qquad \onslide<10->
(1:x):y \qquad \onslide<11->
(2:x)+((1:x):y)
}
\]
\vspace{-2ex}
\end{example}

\end{frame}