# HG changeset patch # User paulson # Date 1077116497 -3600 # Node ID 71dff3bade664cdb3e5ec76bc10bac9466ae9f7e # Parent 386760e884626e5cd9b0711b69d90a4a1694331d new Union syntax diff -r 386760e88462 -r 71dff3bade66 doc-src/TutorialI/Sets/sets.tex --- a/doc-src/TutorialI/Sets/sets.tex Wed Feb 18 10:40:29 2004 +0100 +++ b/doc-src/TutorialI/Sets/sets.tex Wed Feb 18 16:01:37 2004 +0100 @@ -299,7 +299,7 @@ x\isasymin A.\ B} in \textsc{ascii}. Indexed union satisfies this basic law: \begin{isabelle} (b\ \isasymin\ -(\isasymUnion x\isasymin A.\ B\ x))\ =\ (\isasymexists x\isasymin A.\ +(\isasymUnion \isactrlbsub x\isasymin A\isactrlesub \ B\ x) =\ (\isasymexists x\isasymin A.\ b\ \isasymin\ B\ x) \rulenamedx{UN_iff} \end{isabelle} @@ -310,13 +310,11 @@ A;\ b\ \isasymin\ B\ a\isasymrbrakk\ \isasymLongrightarrow\ b\ \isasymin\ -({\isasymUnion}x\isasymin A.\ -B\ x) +(\isasymUnion \isactrlbsub x\isasymin A\isactrlesub \ B\ x) \rulenamedx{UN_I}% \isanewline \isasymlbrakk b\ \isasymin\ -({\isasymUnion}x\isasymin A.\ -B\ x);\ +(\isasymUnion \isactrlbsub x\isasymin A\isactrlesub \ B\ x);\ {\isasymAnd}x.\ {\isasymlbrakk}x\ \isasymin\ A;\ b\ \isasymin\ B\ x\isasymrbrakk\ \isasymLongrightarrow\ @@ -329,7 +327,7 @@ \begin{isabelle} \ \ \ \ \ ({\isasymUnion}x.\ B\ x)\ {\isasymrightleftharpoons}\ -({\isasymUnion}x{\isasymin}UNIV.\ B\ x) +({\isasymUnion}\isactrlbsub x{\isasymin}UNIV\isactrlesub\ B\ x) \end{isabelle} %Abbreviations work as you might expect. The term on the left-hand side of %the \isasymrightleftharpoons\ symbol is automatically translated to the right-hand side when the @@ -351,8 +349,7 @@ theorems are available: \begin{isabelle} (b\ \isasymin\ -({\isasymInter}x\isasymin A.\ -B\ x))\ +(\isasymInter \isactrlbsub x\isasymin A\isactrlesub \ B\ x))\ =\ ({\isasymforall}x\isasymin A.\ b\ \isasymin\ B\ x) @@ -1071,3 +1068,7 @@ two agents in a process algebra is an example of coinduction. The coinduction rule can be strengthened in various ways. \index{fixed points|)} + +%The section "Case Study: Verified Model Checking" is part of this chapter +\input{CTL/ctl} +\endinput