diff -r f3ff2549cdc8 -r 23a118849801 doc-src/TutorialI/Inductive/even-example.tex --- a/doc-src/TutorialI/Inductive/even-example.tex Thu Aug 09 10:17:45 2001 +0200 +++ b/doc-src/TutorialI/Inductive/even-example.tex Thu Aug 09 18:12:15 2001 +0200 @@ -27,7 +27,7 @@ above states that 0 is even; the second states that if $n$ is even, then so is~$n+2$. Given this declaration, Isabelle generates a fixed point definition for \isa{even} and proves theorems about it, -thus following the definitional approach (see \S\ref{sec:definitional}). +thus following the definitional approach (see {\S}\ref{sec:definitional}). These theorems include the introduction rules specified in the declaration, an elimination rule for case analysis and an induction rule. We can refer to these @@ -300,9 +300,10 @@ dispensing with the lemma \isa{even_imp_even_minus_2}. This example also justifies the terminology \textbf{rule inversion}: the new rule inverts the introduction rule -\isa{even.step}. +\isa{even.step}. In general, a rule can be inverted when the set of elements +it introduces is disjoint from those of the other introduction rules. -For one-off applications of rule inversion, use the \isa{ind_cases} method. +For one-off applications of rule inversion, use the \methdx{ind_cases} method. Here is an example: \begin{isabelle} \isacommand{apply}\ (ind_cases\ "Suc(Suc\ n)\ \isasymin \ even")