\chapter{The Tricks of the Trade}

\section{Simplification}
\label{sec:simplification-II}
\index{simplification|(}

\subsection{Advanced features}

\subsubsection{Congruence rules}


\subsubsection{Permutative rewrite rules}

A rewrite rule is \textbf{permutative} if the left-hand side and right-hand
side are the same up to renaming of variables.  The most common permutative
rule is commutativity: $x+y = y+x$.  Another example is $(x-y)-z = (x-z)-y$.
Such rules are problematic because once they apply, they can be used forever.
The simplifier is aware of this danger and treats permutative rules
separately. For details see~\cite{isabelle-ref}.



\subsection{How it works}
\label{sec:SimpHow}

\subsubsection{Higher-order patterns}

\subsubsection{Local assumptions}

\subsubsection{The preprocessor}

\index{simplification|)}


\section{Advanced induction techniques}
\label{sec:advanced-ind}
\input{Misc/document/AdvancedInd.tex}
