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\chapter{Advanced Simplification, Recursion, and Induction}
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\markboth{}{CHAPTER 4: ADVANCED}
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Although we have already learned a lot about simplification, recursion and
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induction, there are some advanced proof techniques that we have not covered
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yet and which are worth knowing about if you intend to beome a serious
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(human) theorem prover. The three sections of this chapter are almost
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independent of each other and can be read in any order. Only the notion of
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\emph{congruence rules}, introduced in the section on simplification, is
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required for parts of the section on recursion.
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\input{document/simp.tex}
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\section{Advanced forms of recursion}
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\label{sec:advanced-recdef}
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\index{*recdef|(}
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\input{../Recdef/document/Nested0.tex}
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\input{../Recdef/document/Nested1.tex}
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\input{../Recdef/document/Nested2.tex}
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\index{*recdef|)}
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\section{Advanced induction techniques}
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\label{sec:advanced-ind}
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\index{induction|(}
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\input{../Misc/document/AdvancedInd.tex}
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\index{induction|)}
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