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\begin{frame}
\small

\begin{definition}
\smallskip
\begin{itemize}
\item
\makebox[25mm][l]{\alert<1>{signature}}
\makebox[20mm][l]{\alert<1>{$\FF$}}
function symbols $f \in \FF$ with arities $\arity{f}$
\medskip
\item<2->
\makebox[25mm][l]{\alert<2>{variables}}
\makebox[20mm][l]{\alert<2>{$\VV$}}
$\FF \cap \VV = \varnothing$ \quad infinitely many
\medskip
\item<3->
\makebox[25mm][l]{\alert<3-6>{terms}}
\makebox[20mm][l]{\alert<3-6>{$\TT(\FF,\VV)$}}
smallest set such that
\begin{itemize}
\item
$\VV \subseteq \TT(\FF,\VV)$
\smallskip
\only{
\item<4-5>
if $f \in \FF$ has arity $0$ then $f \in \TT(\FF,\VV)$
\smallskip
}
\item<5->
if $f \in \FF$ has arity \alert<6>{$n \geqslant \alt<6->{0}{1}$} and
$\seq{t} \in \TT(\FF,\VV)$
then $f(\seq{t}) \in \TT(\FF,\VV)$
\onslide<6->
\only{assuming that $f() = f$}
\end{itemize}
\medskip
\item<7->
\makebox[25mm][l]{\alert<7>{ground terms}}
\makebox[20mm][l]{\alert<7>{$\TT(\FF)$}}
smallest set such that
\begin{itemize}
\item
if $f \in \FF$ has arity $n \geqslant 0$ and
$\seq{t} \in \TT(\FF)$ then $f(\seq{t}) \in \TT(\FF)$
\smallskip
\end{itemize}
\end{itemize}
\end{definition}

\end{frame}