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Mention list$adjacent in DESCRIPTION manual
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mn200 committed Sep 30, 2024
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18 changes: 17 additions & 1 deletion Manual/Description/theories.stex
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%%% -*- Mode: LaTeX; -*-
\newcommand{\subr}{\sb{\mathsf{r}}}
\chapter{Core Theories}\label{HOLtheories}

% LaTeX macros in HOL manuals
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\end{alltt}
\end{hol}
\index{lists, the HOL theory of@lists, the \HOL{} theory of!element adjacency}
The notion of $R$ holding pairwise through a list can be expressed using the predicate \holtxt{adjacent}, where $\holtxt{adjacent}\;\ell\;a\;b$ holds if values $a$ and $b$ appear together (in that order) in list $\ell$.
Then, we have
\begin{hol}
\begin{alltt}
##thm SORTED_adjacent
\end{alltt}
\end{hol}
where the $\subseteq\subr$ relation is the notion of relation-subset (see below on page~\pageref{def:rsubset}).
There are a number of other theorems in \ml{listTheory} about adjacency, including for example:
\begin{hol}
\begin{alltt}
##thm adjacent_REVERSE
##thm adjacent_MAP
\end{alltt}
\end{hol}
\subsubsection{Indexed lists}
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\paragraph{Basic operations}
\newcommand{\subr}{\sb{\mathsf{r}}}
The following basic operations on relations are defined: the empty
relation (\holtxt{EMPTY\_REL}, or $\emptyset\subr$), relation composition (\holtxt{O}, or $\circ\subr$,
infix), inversion (\holtxt{inv}, or $\_^{\mathsf{T}}$ (suffix superscript `T')), domain (\holtxt{RDOM}), and range
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