\begin{frame} \small \begin{definition} \begin{itemize} \item \makebox[3cm][l]{\alert<1,2>{diamond property}} \onslide<3->{\alert<3>{$\diamond$}} \begin{itemize} \item ${\from \cdot \to} \:\subseteq\: {\to \cdot \from}$ \smallskip \item<2-> \hspace{-1mm}\begin{tikzpicture}[on grid,baseline=(1).baseline] \node (1) {$\strut a$}; \node (2) [below left=of 1] {$b$}; \node (3) [below right=of 1] {$c$}; \node (4) [below right=of 2] {$\strut d$}; \node (5) [left=of 1] {\makebox[3cm][l]{$\strut \forall a,b,c$}}; \node (6) [left=of 4] {\makebox[3cm][l]{$\strut \exists d$}}; \draw[->] (1) -- (2); \draw[->] (1) -- (3); \draw[dotted,->] (2) -- (4); \draw[dotted,->] (3) -- (4); \end{tikzpicture} \end{itemize} \end{itemize} \end{definition} \bigskip \begin{lemma}<4-> \smallskip An ARS $\AA = \ARS$ is confluent if ${\to}$ has the diamond property. \smallskip \end{lemma} \onslide<5-> \begin{proof} Exercise. \end{proof} \end{frame}