doc-src/TutorialI/CTL/document/CTLind.tex
changeset 10845 3696bc935bbd
parent 10795 9e888d60d3e5
child 10855 140a1ed65665
equal deleted inserted replaced
10844:0c0e7de7e9c5 10845:3696bc935bbd
   123 \begin{isabelle}%
   123 \begin{isabelle}%
   124 \ \ \ \ \ {\isasymlbrakk}{\isasymforall}p{\isasymin}Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharsemicolon}\ t\ {\isasymin}\ Avoid\ s\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}%
   124 \ \ \ \ \ {\isasymlbrakk}{\isasymforall}p{\isasymin}Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharsemicolon}\ t\ {\isasymin}\ Avoid\ s\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}%
   125 \end{isabelle}
   125 \end{isabelle}
   126 The main theorem is simply the corollary where \isa{t\ {\isacharequal}\ s},
   126 The main theorem is simply the corollary where \isa{t\ {\isacharequal}\ s},
   127 in which case the assumption \isa{t\ {\isasymin}\ Avoid\ s\ A} is trivially true
   127 in which case the assumption \isa{t\ {\isasymin}\ Avoid\ s\ A} is trivially true
   128 by the first \isa{Avoid}-rule). Isabelle confirms this:%
   128 by the first \isa{Avoid}-rule. Isabelle confirms this:%
   129 \end{isamarkuptext}%
   129 \end{isamarkuptext}%
   130 \isacommand{theorem}\ AF{\isacharunderscore}lemma{\isadigit{2}}{\isacharcolon}\isanewline
   130 \isacommand{theorem}\ AF{\isacharunderscore}lemma{\isadigit{2}}{\isacharcolon}\isanewline
   131 \ \ {\isachardoublequote}{\isacharbraceleft}s{\isachardot}\ {\isasymforall}p\ {\isasymin}\ Paths\ s{\isachardot}\ {\isasymexists}\ i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharbraceright}\ {\isasymsubseteq}\ lfp{\isacharparenleft}af\ A{\isacharparenright}{\isachardoublequote}\isanewline
   131 \ \ {\isachardoublequote}{\isacharbraceleft}s{\isachardot}\ {\isasymforall}p\ {\isasymin}\ Paths\ s{\isachardot}\ {\isasymexists}\ i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharbraceright}\ {\isasymsubseteq}\ lfp{\isacharparenleft}af\ A{\isacharparenright}{\isachardoublequote}\isanewline
   132 \isacommand{by}{\isacharparenleft}auto\ elim{\isacharcolon}Avoid{\isacharunderscore}in{\isacharunderscore}lfp\ intro{\isacharcolon}Avoid{\isachardot}intros{\isacharparenright}\isanewline
   132 \isacommand{by}{\isacharparenleft}auto\ elim{\isacharcolon}Avoid{\isacharunderscore}in{\isacharunderscore}lfp\ intro{\isacharcolon}Avoid{\isachardot}intros{\isacharparenright}\isanewline
   133 \isanewline
   133 \isanewline