<commit_before>%\chapter{The Tricks of the Trade}
\chapter{Advanced Simplification, Recursion, and Induction}
\markboth{}{CHAPTER 4: ADVANCED}

Although we have already learned a lot about simplification, recursion and
induction, there are some advanced proof techniques that we have not covered
yet and which are worth knowing about if you intend to beome a serious
(human) theorem prover. The three sections of this chapter are almost
independent of each other and can be read in any order. Only the notion of
\emph{congruence rules}, introduced in the section on simplification, is
required for parts of the section on recursion.

\input{Advanced/document/simp.tex}

\section{Advanced forms of recursion}
\label{sec:advanced-recdef}
\index{*recdef|(}
\input{Recdef/document/Nested0.tex}
\input{Recdef/document/Nested1.tex}
\input{Recdef/document/Nested2.tex}
\index{*recdef|)}

\section{Advanced induction techniques}
\label{sec:advanced-ind}
\input{Misc/document/AdvancedInd.tex}<commit_msg>*** empty log message ***<commit_after>%\chapter{The Tricks of the Trade}
\chapter{Advanced Simplification, Recursion, and Induction}
\markboth{}{CHAPTER 4: ADVANCED}

Although we have already learned a lot about simplification, recursion and
induction, there are some advanced proof techniques that we have not covered
yet and which are worth knowing about if you intend to beome a serious
(human) theorem prover. The three sections of this chapter are almost
independent of each other and can be read in any order. Only the notion of
\emph{congruence rules}, introduced in the section on simplification, is
required for parts of the section on recursion.

\input{Advanced/document/simp.tex}

\section{Advanced forms of recursion}
\label{sec:advanced-recdef}
\index{*recdef|(}
\input{Recdef/document/Nested0.tex}
\input{Recdef/document/Nested1.tex}
\input{Recdef/document/Nested2.tex}
\index{*recdef|)}

\section{Advanced induction techniques}
\label{sec:advanced-ind}
\index{induction|(}
\input{Misc/document/AdvancedInd.tex}
\index{induction|)}
{'fraction_non_alphanumeric': 0.0940254652301665, 'fraction_numerical': 0.0039177277179236044, 'mean_word_length': 5.742574257425742, 'pattern_counts': {'":': 0, '<': 3, '<?xml version=': 0, '>': 3, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '7292252', 'n_tokens_mistral': 634, 'n_tokens_neox': 594, 'n_words': 223}