76/250
\begin{frame}
\small

\begin{definition}[Derived Relations of $\to$]
\begin{itemize}[<+->]

\item
\makebox[2cm][l]{\alert<1>{$\from$} or \alert<1>{$\to^{-1}$}}
inverse of $\to$
\item
\makebox[2cm][l]{\alert<2>{$\to^=$}}
reflexive closure of $\to$
\item
\makebox[2cm][l]{\alert<3>{$\to^+$}}
transitive closure of $\to$
\item
\makebox[2cm][l]{\alert<4>{$\to^*$} or \alert<4>{$\twoheadrightarrow$}}
transitive and reflexive closure of $\to$
\item
\makebox[2cm][l]{\alert<5>{$\FromP{*}$} or \alert<5>{$\twoheadleftarrow$}}
\makebox[22mm][l]{inverse of $\to^*$}
(transitive and reflexive closure of $\from$)
\item
\makebox[2cm][l]{\alert<6>{$\fromto$}}
symmetric closure of $\to$, that is, ${\fromto} = {\to} \cup {\from}$
\item
\makebox[2cm][l]{\alert<7>{$\conv$}}
\makebox[22mm][l]{\alert<7>{conversion}}
(equivalence relation generated by $\to$)
\item
\makebox[2cm][l]{\alert<8>{$\join$}}
\makebox[22mm][l]{\alert<8>{joinability}}
${\join} = {\to^* \cdot \FromP{*}}$
\item
\makebox[2cm][l]{\alert<9>{$\uparrow$}}
\makebox[22mm][l]{\alert<9>{meetability}}
${\uparrow} = {\FromP{*} \cdot \to^*}$
\end{itemize}
\end{definition}

\medskip
\begin{minipage}{.2\textwidth}
\only<2->{a relation $R$ is}\ \\\ \\\ \\ 
\end{minipage}
\begin{minipage}{.69\textwidth}
\begin{itemize}
  \item<2-> \alert<2,7>{reflexive} if $a \mathrel{R} a$ for all $a \in A$,
  \item<3-> \alert<3,7>{transitive} if $a \mathrel{R} c$ whenenver $a \mathrel{R} b$ and $b \mathrel{R} c$,
  \item<6-> \alert<6,7>{symmetric} if $a \mathrel{R} b$ whenenver $b \mathrel{R} a$.
\end{itemize}
\end{minipage}
\bigskip

\end{frame}