diff -r c452fea3ce74 -r 499637e8f2c6 doc-src/TutorialI/Misc/AdvancedInd.thy --- a/doc-src/TutorialI/Misc/AdvancedInd.thy Wed Oct 11 00:03:22 2000 +0200 +++ b/doc-src/TutorialI/Misc/AdvancedInd.thy Wed Oct 11 09:09:06 2000 +0200 @@ -275,13 +275,18 @@ by(insert induct_lem, blast); text{* + Finally we should mention that HOL already provides the mother of all -inductions, \emph{wellfounded induction} (@{thm[source]wf_induct}): -@{thm[display]"wf_induct"[no_vars]} -where @{term"wf r"} means that the relation @{term"r"} is wellfounded. +inductions, \textbf{wellfounded +induction}\indexbold{induction!wellfounded}\index{wellfounded +induction|see{induction, wellfounded}} (@{thm[source]wf_induct}): +@{thm[display]wf_induct[no_vars]} +where @{term"wf r"} means that the relation @{term r} is wellfounded +(see \S\ref{sec:wellfounded}). For example, theorem @{thm[source]nat_less_induct} can be viewed (and derived) as a special case of @{thm[source]wf_induct} where -@{term"r"} is @{text"<"} on @{typ"nat"}. For details see the library. +@{term r} is @{text"<"} on @{typ nat}. The details can be found in the HOL library. +For a mathematical account of wellfounded induction see, for example, \cite{Baader-Nipkow}. *}; (*<*)