<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">
\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\definecolor{ugreen}{rgb}{0,0.5,0}

%%% outline
%-------------------------------------------------------------------------


\begin{tikzpicture}

{\footnotesize
\node [anchor=west] (mid) at (0,0) {$\alpha(1,0)\alpha(2,0) + \alpha(1,0)\alpha(2,1) + \alpha(1,0)\alpha(2,2) +$};
\node [anchor=west] (mid2) at ([yshift=-2em]mid.west) {$\alpha(1,1)\alpha(2,0) + \alpha(1,1)\alpha(2,1) + \alpha(1,1)\alpha(2,2)+$};
\node [anchor=west] (mid3) at ([yshift=-2em]mid2.west) {$\alpha(1,2)\alpha(2,0) + \alpha(1,2)\alpha(2,1) + \alpha(1,2)\alpha(2,2)$};
}

\begin{pgfonlayer}{background}
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (mid) (mid2) (mid3)] (exampleeq) {};
\end{pgfonlayer}

{\footnotesize
{
\node [anchor=north] (eq1) at ([xshift=2em,yshift=-2em]exampleeq.south west) {$\sum\limits_{y_1=0}^{2} \sum\limits_{y_2=0}^{2} \alpha(1,y_1)\alpha(2,y_2)$};
\node [anchor=west] (eq1part2) at ([xshift=-1em,yshift=-3em]eq1.west) {$=$};
\node [anchor=west] (eq1part3) at ([xshift=-0.5em]eq1part2.east) {$\sum\limits_{y_1=0}^{2} \sum\limits_{y_2=0}^{2} \prod\limits_{x=1}^{2} $};
\node [anchor=west,inner sep=2pt] (eq1part4) at ([xshift=-0.3em]eq1part3.east) {};
}

{
\node [anchor=north] (eq2) at ([xshift=-2em,yshift=-2em]exampleeq.south east) {$(\alpha(1,0)+\alpha(1,1)+\alpha(1,2))\cdot$};
\node [anchor=west] (eq2part2) at ([yshift=-1.5em]eq2.west) {$(\alpha(2,0)+\alpha(2,1)+\alpha(2,2))$};
\node [anchor=west] (eq2part3) at ([xshift=2.1in]eq1part2.east){$=$};
\node [anchor=west] (eq2part4) at ([xshift=-0.5em]eq2part3.east){$\prod\limits_{x=1}^{2} \sum\limits_{y=0}^{2}$};
\node [anchor=west,inner sep=2pt] (eq2part5) at ([xshift=-0.3em]eq2part4.east){};
}
}

\begin{pgfonlayer}{background}
{
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (eq1) (eq1part2) (eq1part3)] (eq1full) {};
}
{
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (eq2) (eq2part2) (eq2part3) (eq2part4)] (eq2full) {};
}
\end{pgfonlayer}

{
\draw [-&gt;,thick] ([xshift=-3em]exampleeq.south) .. controls +(south:1.5em) and +(north:1.5em) .. (eq1full.north);
}
{
\draw [-&gt;,thick] ([xshift=3em]exampleeq.south) .. controls +(south:1.5em) and +(north:1.5em) .. (eq2full.north);
}

{
\node [anchor=west] at ([xshift=0.7em]eq1full.east) {\LARGE{\textbf{=}}};
}

{
{\large
\node [anchor=west] (feq) at ([xshift=3em,yshift=-3em]eq1full.south west) {$\sum\limits_{a_1=0}^{l} ... \sum\limits_{a_m=0}^{l} \prod\limits_{j=1}^{m}$};
\node [anchor=west,inner sep=2pt,fill=blue!20] (feqpart2) at ([xshift=-0.3em]feq.east) {$f(s_j|t_{a_j})$};
\node [anchor=west,inner sep=1pt] (feqpart3) at (feqpart2.east) {=};
\node [anchor=west] (feqpart4) at (feqpart3.east) {$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l}$};
\node [anchor=west,inner sep=2pt,fill=blue!20] (feqpart5) at ([xshift=-0.3em]feqpart4.east) {$f(s_j|t_i)$};
}

\draw [-&gt;,thick] ([xshift=1.4em]eq1part4.south) .. controls +(south:2.5em) and +(north:2.5em) .. (feqpart2.north);
\draw [-&gt;,thick] ([xshift=1.2em]eq2part5.south) .. controls +(south:1.5em) and +(north:1.5em) .. (feqpart5.north);

\node [anchor=west,inner sep=2pt,fill=blue!20] (eq1part4) at ([xshift=-0.3em]eq1part3.east) {\footnotesize{$\alpha(x,y_x)$}};
\node [anchor=west,inner sep=2pt,fill=blue!20] (eq2part5) at ([xshift=-0.3em]eq2part4.east){\footnotesize{$\alpha(x,y)$}};

}

\end{tikzpicture}


</pre></body></html>