diff -r e928bdf62014 -r e61e7e1eacaf doc-src/TutorialI/CTL/document/CTL.tex --- a/doc-src/TutorialI/CTL/document/CTL.tex Fri Oct 13 11:15:56 2000 +0200 +++ b/doc-src/TutorialI/CTL/document/CTL.tex Fri Oct 13 18:02:08 2000 +0200 @@ -5,6 +5,7 @@ \isamarkupsubsection{Computation tree logic---CTL} % \begin{isamarkuptext}% +\label{sec:CTL} The semantics of PDL only needs transitive reflexive closure. Let us now be a bit more adventurous and introduce a new temporal operator that goes beyond transitive reflexive closure. We extend the datatype @@ -265,9 +266,13 @@ \ \isacommand{apply}{\isacharparenleft}auto\ dest{\isacharcolon}not{\isacharunderscore}in{\isacharunderscore}lfp{\isacharunderscore}afD{\isacharparenright}\isanewline \isacommand{done}% \begin{isamarkuptext}% -The main theorem is proved as for PDL, except that we also derive the necessary equality -\isa{lfp{\isacharparenleft}af\ A{\isacharparenright}\ {\isacharequal}\ {\isachardot}{\isachardot}{\isachardot}} by combining \isa{AF{\isacharunderscore}lemma{\isadigit{1}}} and \isa{AF{\isacharunderscore}lemma{\isadigit{2}}} -on the spot:% +If you found the above proofs somewhat complicated we recommend you read +\S\ref{sec:CTL-revisited} where we shown how inductive definitions lead to +simpler arguments. + +The main theorem is proved as for PDL, except that we also derive the +necessary equality \isa{lfp{\isacharparenleft}af\ A{\isacharparenright}\ {\isacharequal}\ {\isachardot}{\isachardot}{\isachardot}} by combining +\isa{AF{\isacharunderscore}lemma{\isadigit{1}}} and \isa{AF{\isacharunderscore}lemma{\isadigit{2}}} on the spot:% \end{isamarkuptext}% \isacommand{theorem}\ {\isachardoublequote}mc\ f\ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ s\ {\isasymTurnstile}\ f{\isacharbraceright}{\isachardoublequote}\isanewline \isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ f{\isacharparenright}\isanewline