|
9933
|
1 |
%\chapter{The Tricks of the Trade}
|
|
|
2 |
\chapter{Advanced Simplification, Recursion, and Induction}
|
|
|
3 |
\markboth{}{CHAPTER 4: ADVANCED}
|
|
9743
|
4 |
|
|
9933
|
5 |
Although we have already learned a lot about simplification, recursion and
|
|
|
6 |
induction, there are some advanced proof techniques that we have not covered
|
|
|
7 |
yet and which are worth knowing about if you intend to beome a serious
|
|
|
8 |
(human) theorem prover. The three sections of this chapter are almost
|
|
|
9 |
independent of each other and can be read in any order. Only the notion of
|
|
|
10 |
\emph{congruence rules}, introduced in the section on simplification, is
|
|
|
11 |
required for parts of the section on recursion.
|
|
9743
|
12 |
|
|
9933
|
13 |
\input{Advanced/document/simp.tex}
|
|
9743
|
14 |
|
|
9933
|
15 |
\section{Advanced forms of recursion}
|
|
|
16 |
\label{sec:advanced-recdef}
|
|
|
17 |
\index{*recdef|(}
|
|
|
18 |
\input{Recdef/document/Nested0.tex}
|
|
|
19 |
\input{Recdef/document/Nested1.tex}
|
|
|
20 |
\input{Recdef/document/Nested2.tex}
|
|
|
21 |
\index{*recdef|)}
|
|
9743
|
22 |
|
|
|
23 |
\section{Advanced induction techniques}
|
|
|
24 |
\label{sec:advanced-ind}
|
|
|
25 |
\input{Misc/document/AdvancedInd.tex}
|