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\noindent{\sc Event}:   Start with the library {\tt{"arith"}}.

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\begin{verbatim}; Here again is the definition of RAMSEY.

\end{verbatim}\begin{tabbing}{\sc Definition}:\index{ramsey} \\  
\=\+{\rm{ramsey}}\,({\it{p\/}}, {\it{q\/}})\index{ramsey} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{p\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{1}} \\ 
{\bf elseif }{\it{q\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\rm{ramsey}}\,({\it{p\/}} $-\;1$, {\it{q\/}})\index{ramsey} $+$ {\rm{ramsey}}\,({\it{p\/}}, {\it{q\/}} $-\;1$)\index{ramsey}$\;${\bf  endif}\-\-
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\begin{tabbing}{\sc Definition}:\index{fact} \\  
\=\+{\rm{fact}}\,({\it{n\/}})\index{fact} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\it{n\/}} $*$ {\rm{fact}}\,({\it{n\/}} $-\;1$)\index{fact}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{choose} \\  
{\rm{choose}}\,({\it{m\/}}, {\it{n\/}})\index{choose} $=$ ({\rm{fact}}\,({\it{m\/}})\index{fact} $\div$ ({\rm{fact}}\,({\it{n\/}})\index{fact} $*$ {\rm{fact}}\,({\it{m\/}} $-$ {\it{n\/}})\index{fact}))
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\begin{tabbing}{\sc Theorem}:  fact-not-zerop \\ \index{fact-not-zerop}
{\rm{fact}}\,({\it{x\/}})\index{fact} $\not=$ {\tt{0}}
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\begin{tabbing}{\sc Theorem}:  ramsey-choose-1 \\ \index{ramsey-choose-1}
(({\rm{fact}}\,({\it{p\/}})\index{fact} $*$ {\rm{fact}}\,({\it{q\/}})\index{fact}) $*$ {\rm{ramsey}}\,({\it{p\/}}, {\it{q\/}})\index{ramsey}) $=$ {\rm{fact}}\,({\it{p\/}} $+$ {\it{q\/}})\index{fact}
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\begin{tabbing}{\sc Theorem}:  ramsey-choose \\ \index{ramsey-choose}
{\rm{ramsey}}\,({\it{p\/}}, {\it{q\/}})\index{ramsey} $=$ {\rm{choose}}\,({\it{p\/}} $+$ {\it{q\/}}, {\it{p\/}})\index{choose}
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