\begin{frame} \small \begin{definition}[Positions] \begin{itemize} \item \alert<1>{$\Pos(\:\cdot\:)$}, the set of \alert<1>{positions of a term}\\[1ex] \( \Pos(t) = \begin{cases} \{ \epsilon \} & \text{if $t \in \VV$} \\[.5ex] \{ \epsilon \} \cup \{ ip \mid p \in \Pos(t_i) \} & \text{if $t = f(\seq{t})$} \end{cases} \) \end{itemize} \end{definition} \bigskip \begin{example}<2-> \GREEN{$(2:x)+((1:x):y)$} \qquad \GREEN{\begin{tikzpicture}[on grid,baseline=(1).baseline] \matrix[ampersand replacement=\&,row sep=5mm,column sep=2mm]{ \& \& \& \node (1) {$+$}; \& \& \& \\ \& \node (2) {$:$}; \& \& \& \& \node (3) {$:$}; \& \\ \node (4) {$2$}; \& \& \node (5) {$x$}; \& \& \node (6) {$:$}; \& \& \node (7) {$y$}; \\ \& \& \& \node (8) {$1$}; \& \& \node (9) {$x$}; \& \\}; \draw (1) -- (2) (1) -- (3); \draw (2) -- (4) (2) -- (5); \draw (3) -- (6) (3) -- (7); \draw (6) -- (8) (6) -- (9); \onslide<3->{ \draw (1) node[right] {\alert<3>{$\,{}^\epsilon$}}; \draw (2) node[left] {\alert<3>{${}^1\,$}}; \draw (3) node[right] {\alert<3>{$\,{}^2$}}; \draw (4) node[left] {\alert<3>{${}^{11}\,$}}; \draw (5) node[right] {\alert<3>{$\,{}^{12}$}}; \draw (6) node[left] {\alert<3>{${}^{21}\,$}}; \draw (7) node[right] {\alert<3>{$\,{}^{22}$}}; \draw (8) node[left] {\alert<3>{${}^{211}\,$}}; \draw (9) node[right] {\alert<3>{$\,{}^{212}$}}; } \end{tikzpicture}} \end{example} \end{frame}