\begin{frame}
  \small
  
  \vspace{-1ex}
  
  \begin{definition}
  Let $\AA = \langle A, \to_1,\to_2 \rangle$ be an ARS.
  \begin{itemize}
  \item
    \alert<1-2>{$\to_1$ commutes with $\to_2$}
    \begin{itemize}
    \item
      ${\FromBP{2}{*} \cdot \to_1^*} \:\subseteq\: {\to_1^* \cdot \FromBP{2}{*}}$
      \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[->>,blue!75!black] (1) -- (2) node [midway,above left] {$2$};
      \draw[->>,green!50!black] (1) -- (3) node [midway,above right] {$1$};
      \draw[dotted,->>,green!50!black] (2) -- (4) node [midway,below left] {$1$};
      \draw[dotted,->>,blue!75!black] (3) -- (4) node [midway,below right] {$2$};
      \end{tikzpicture}
   \end{itemize}
  \item<3->
    \alert<3-4>{$\to_1$ commutes weakly with $\to_2$}
    \begin{itemize}
    \item
      ${\FromBP{2}{} \cdot \to_1} \:\subseteq\: {\to_1^* \cdot \FromBP{2}{*}}$
      \smallskip
    \item<4->
      \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[->,blue!75!black] (1) -- (2) node [midway,above left] {$2$};
      \draw[->,green!50!black] (1) -- (3) node [midway,above right] {$1$};
      \draw[dotted,->>,green!50!black] (2) -- (4) node [midway,below left] {$1$};
      \draw[dotted,->>,blue!75!black] (3) -- (4) node [midway,below right] {$2$};
      \end{tikzpicture}
    \end{itemize}
  \end{itemize}
  \end{definition}
\end{frame}