diff -r cb3612cc41a3 -r fc075ae929e4 doc-src/TutorialI/Inductive/document/Mutual.tex --- a/doc-src/TutorialI/Inductive/document/Mutual.tex Sun Jan 30 20:48:50 2005 +0100 +++ b/doc-src/TutorialI/Inductive/document/Mutual.tex Tue Feb 01 18:01:57 2005 +0100 @@ -39,27 +39,8 @@ \end{isamarkuptext}% \isamarkuptrue% \isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}m\ {\isasymin}\ even\ {\isasymlongrightarrow}\ {\isadigit{2}}\ dvd\ m{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}n\ {\isasymin}\ odd\ {\isasymlongrightarrow}\ {\isadigit{2}}\ dvd\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isamarkupfalse% -% -\begin{isamarkuptxt}% -\noindent -The proof is by rule induction. Because of the form of the induction theorem, -it is applied by \isa{rule} rather than \isa{erule} as for ordinary -inductive definitions:% -\end{isamarkuptxt}% \isamarkuptrue% -\isacommand{apply}{\isacharparenleft}rule\ even{\isacharunderscore}odd{\isachardot}induct{\isacharparenright}\isamarkupfalse% -% -\begin{isamarkuptxt}% -\begin{isabelle}% -\ {\isadigit{1}}{\isachardot}\ {\isadigit{2}}\ dvd\ {\isadigit{0}}\isanewline -\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ odd{\isacharsemicolon}\ {\isadigit{2}}\ dvd\ Suc\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isadigit{2}}\ dvd\ Suc\ n\isanewline -\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ Mutual{\isachardot}even{\isacharsemicolon}\ {\isadigit{2}}\ dvd\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isadigit{2}}\ dvd\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}% -\end{isabelle} -The first two subgoals are proved by simplification and the final one can be -proved in the same manner as in \S\ref{sec:rule-induction} -where the same subgoal was encountered before. -We do not show the proof script.% -\end{isamarkuptxt}% +\isamarkupfalse% \isamarkuptrue% \isamarkupfalse% \isamarkupfalse%