diff -r e8aa81362f41 -r 1bece7f35762 doc-src/TutorialI/CTL/document/CTL.tex --- a/doc-src/TutorialI/CTL/document/CTL.tex Thu Oct 12 18:06:31 2000 +0200 +++ b/doc-src/TutorialI/CTL/document/CTL.tex Thu Oct 12 18:09:06 2000 +0200 @@ -62,7 +62,7 @@ by simplification and clarification% \end{isamarkuptxt}% \isacommand{apply}{\isacharparenleft}rule\ subsetI{\isacharparenright}\isanewline -\isacommand{apply}{\isacharparenleft}erule\ Lfp{\isachardot}induct{\isacharbrackleft}OF\ {\isacharunderscore}\ mono{\isacharunderscore}af{\isacharbrackright}{\isacharparenright}\isanewline +\isacommand{apply}{\isacharparenleft}erule\ lfp{\isacharunderscore}induct{\isacharbrackleft}OF\ {\isacharunderscore}\ mono{\isacharunderscore}af{\isacharbrackright}{\isacharparenright}\isanewline \isacommand{apply}{\isacharparenleft}clarsimp\ simp\ add{\isacharcolon}\ af{\isacharunderscore}def\ Paths{\isacharunderscore}def{\isacharparenright}% \begin{isamarkuptxt}% \noindent @@ -120,7 +120,7 @@ \begin{isamarkuptext}% \noindent is proved by a variant of contraposition (\isa{swap}: -\isa{{\isasymlbrakk}{\isasymnot}\ Pa{\isacharsemicolon}\ {\isasymnot}\ P\ {\isasymLongrightarrow}\ Pa{\isasymrbrakk}\ {\isasymLongrightarrow}\ P}), i.e.\ assuming the negation of the conclusion +\isa{{\isasymlbrakk}{\isasymnot}\ Q{\isacharsemicolon}\ {\isasymnot}\ P\ {\isasymLongrightarrow}\ Q{\isasymrbrakk}\ {\isasymLongrightarrow}\ P}), i.e.\ assuming the negation of the conclusion and proving \isa{s\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}}. Unfolding \isa{lfp} once and simplifying with the definition of \isa{af} finishes the proof.