# HG changeset patch # User nipkow # Date 973270620 -3600 # Node ID d72638f2b78e6d74fbcaa9ace33840062b2a7427 # Parent f9211fc8cd7dbb720234a531efdf84bcfe7721ee *** empty log message *** diff -r f9211fc8cd7d -r d72638f2b78e doc-src/TutorialI/Sets/sets.tex --- a/doc-src/TutorialI/Sets/sets.tex Fri Nov 03 17:14:06 2000 +0100 +++ b/doc-src/TutorialI/Sets/sets.tex Fri Nov 03 17:57:00 2000 +0100 @@ -883,13 +883,15 @@ Intuitively, the relation~$\prec$ is \textbf{well-founded} if it admits no infinite descending chains $\cdots \prec a@2 \prec a@1 \prec a@0.$ -If $\prec$ is well-founded then it can be used with the well-founded -induction rule: +If $\prec$ is well-founded then it can be used with the \textbf{well-founded +induction}\indexbold{induction!well-founded}\index{well-founded +induction|see{induction, well-founded}} rule: $\infer{P(a)}{\infer*{P(x)}{[\forall y.\, y\prec x \imp P(y)]}}$ To show $P(a)$ for a particular term~$a$, it suffices to show $P(x)$ for arbitrary~$x$ under the assumption that $P(y)$ holds for $y\prec x$. Intuitively, the well-foundedness of $\prec$ ensures that the chains of -reasoning are finite. +reasoning are finite. For a fuller account of well-founded relations and +induction see, for example, \cite{Baader-Nipkow}. In Isabelle, the induction rule is expressed like this: \begin{isabelle}