\section{The Theory {\tt suc}}

The theory \ml{suc}\index{suc, theory@{\ptt suc}, theory} contains an
\adhoc\ collection of 
theorems about \ml{SUC}. It contains no new definitions.
The theorems that have been pre-proved in this theory include but are not
restricted to the following:
\begin{hol}
\index{NOT\_SUC\_LESS\_EQ\_0@{\ptt NOT\_SUC\_LESS\_EQ\_0}}
\index{SUC\_GREATER\_EQ\_SUC@{\ptt SUC\_GREATER\_EQ\_SUC}}
\index{NOT\_SUC\_LESS\_EQ\_SELF@{\ptt NOT\_SUC\_LESS\_EQ\_SELF}}
\index{SUC\_NOT\_0@{\ptt SUC\_NOT\_0}}
\begin{verbatim}
  NOT_SUC_LESS_EQ_0     |- !n. ~(SUC n) <= 0

  SUC_GREATER_EQ_SUC    |- !n m. (SUC m) >= (SUC n) = m >= n

  NOT_SUC_LESS_EQ_SELF  |- !n. ~(SUC n) <= n

  SUC_NOT_0             |- !n. ~(SUC n = 0)
\end{verbatim}\end{hol}
