diff -r c452fea3ce74 -r 499637e8f2c6 doc-src/TutorialI/Misc/document/AdvancedInd.tex --- a/doc-src/TutorialI/Misc/document/AdvancedInd.tex Wed Oct 11 00:03:22 2000 +0200 +++ b/doc-src/TutorialI/Misc/document/AdvancedInd.tex Wed Oct 11 09:09:06 2000 +0200 @@ -251,14 +251,18 @@ \isacommand{by}{\isacharparenleft}insert\ induct{\isacharunderscore}lem{\isacharcomma}\ blast{\isacharparenright}% \begin{isamarkuptext}% Finally we should mention that HOL already provides the mother of all -inductions, \emph{wellfounded induction} (\isa{wf{\isacharunderscore}induct}): +inductions, \textbf{wellfounded +induction}\indexbold{induction!wellfounded}\index{wellfounded +induction|see{induction, wellfounded}} (\isa{wf{\isacharunderscore}induct}): \begin{isabelle}% \ \ \ \ \ {\isasymlbrakk}wf\ r{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ {\isasymforall}y{\isachardot}\ {\isacharparenleft}y{\isacharcomma}\ x{\isacharparenright}\ {\isasymin}\ r\ {\isasymlongrightarrow}\ P\ y\ {\isasymLongrightarrow}\ P\ x{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ a% \end{isabelle} -where \isa{wf\ r} means that the relation \isa{r} is wellfounded. +where \isa{wf\ r} means that the relation \isa{r} is wellfounded +(see \S\ref{sec:wellfounded}). For example, theorem \isa{nat{\isacharunderscore}less{\isacharunderscore}induct} can be viewed (and derived) as a special case of \isa{wf{\isacharunderscore}induct} where -\isa{r} is \isa{{\isacharless}} on \isa{nat}. For details see the library.% +\isa{r} is \isa{{\isacharless}} on \isa{nat}. The details can be found in the HOL library. +For a mathematical account of wellfounded induction see, for example, \cite{Baader-Nipkow}.% \end{isamarkuptext}% \end{isabellebody}% %%% Local Variables: