doc-src/TutorialI/fp.tex
 changeset 9754 a123a64cadeb parent 9742 98d3ca2c18f7 child 9792 bbefb6ce5cb2
--- a/doc-src/TutorialI/fp.tex	Wed Aug 30 18:05:20 2000 +0200
+++ b/doc-src/TutorialI/fp.tex	Wed Aug 30 18:09:20 2000 +0200
@@ -405,16 +405,12 @@

Simplification is one of the central theorem proving tools in Isabelle and
many other systems. The tool itself is called the \bfindex{simplifier}. The
-purpose of this section is twofold: to introduce the many features of the
-simplifier (\S\ref{sec:SimpFeatures}) and to explain a little bit how the
-simplifier works (\S\ref{sec:SimpHow}).  Anybody intending to use HOL should
-\S\ref{sec:SimpHow} as well in order to understand what happened in case
-things do not simplify as expected.
-
-
-\subsection{Using the simplifier}
-\label{sec:SimpFeatures}
+purpose of this section is introduce the many features of the simplifier.
+Anybody intending to use HOL should read this section. Later on
+(\S\ref{sec:simplification-II}) we explain some more advanced features and a
+little bit of how the simplifier works. The serious student should read that
+section as well, in particular in order to understand what happened if things
+do not simplify as expected.

\subsubsection{What is simplification}

@@ -572,11 +568,11 @@
inductive proofs. The first one we have already mentioned in our initial
example:
\begin{quote}
-{\em 1. Theorems about recursive functions are proved by induction.}
+\emph{Theorems about recursive functions are proved by induction.}
\end{quote}
In case the function has more than one argument
\begin{quote}
-{\em 2. Do induction on argument number $i$ if the function is defined by
+\emph{Do induction on argument number $i$ if the function is defined by
recursion in argument number $i$.}
\end{quote}
When we look at the proof of {\makeatother\isa{(xs @ ys) @ zs = xs @ (ys @
@@ -598,8 +594,8 @@
side, the simpler \isa{rev} on the right-hand side. This constitutes
another, albeit weak heuristic that is not restricted to induction:
\begin{quote}
-  {\em 5. The right-hand side of an equation should (in some sense) be
-    simpler than the left-hand side.}
+  \emph{The right-hand side of an equation should (in some sense) be simpler
+    than the left-hand side.}
\end{quote}
The heuristic is tricky to apply because it is not obvious that
\isa{rev xs \at\ ys} is simpler than \isa{itrev xs ys}. But see what