diff -r a5f86aed785b -r a977245dfc8a doc-src/TutorialI/Misc/document/Itrev.tex --- a/doc-src/TutorialI/Misc/document/Itrev.tex Tue Aug 29 15:43:29 2000 +0200 +++ b/doc-src/TutorialI/Misc/document/Itrev.tex Tue Aug 29 16:05:13 2000 +0200 @@ -31,9 +31,9 @@ \begin{isamarkuptxt}% \noindent Unfortunately, this is not a complete success: -\begin{isabellepar}% +\begin{isabelle} ~1.~\dots~itrev~list~[]~=~rev~list~{\isasymLongrightarrow}~itrev~list~[a]~=~rev~list~@~[a]% -\end{isabellepar}% +\end{isabelle} Just as predicted above, the overall goal, and hence the induction hypothesis, is too weak to solve the induction step because of the fixed \isa{[]}. The corresponding heuristic: @@ -57,11 +57,11 @@ Although we now have two variables, only \isa{xs} is suitable for induction, and we repeat our above proof attempt. Unfortunately, we are still not there: -\begin{isabellepar}% +\begin{isabelle} ~1.~{\isasymAnd}a~list.\isanewline ~~~~~~~itrev~list~ys~=~rev~list~@~ys~{\isasymLongrightarrow}\isanewline ~~~~~~~itrev~list~(a~\#~ys)~=~rev~list~@~a~\#~ys% -\end{isabellepar}% +\end{isabelle} The induction hypothesis is still too weak, but this time it takes no intuition to generalize: the problem is that \isa{ys} is fixed throughout the subgoal, but the induction hypothesis needs to be applied with