doc-src/TutorialI/Sets/sets.tex
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   385 \isa{\isasymexists z\isasymin A.\ P\ x}.  For indexed unions and
   385 \isa{\isasymexists z\isasymin A.\ P\ x}.  For indexed unions and
   386 intersections, you may see the constants 
   386 intersections, you may see the constants 
   387 \cdx{UNION} and  \cdx{INTER}\@.
   387 \cdx{UNION} and  \cdx{INTER}\@.
   388 The internal constant for $\varepsilon x.P(x)$ is~\cdx{Eps}.
   388 The internal constant for $\varepsilon x.P(x)$ is~\cdx{Eps}.
   389 
   389 
   390 We have only scratched the surface of Isabelle/HOL's set theory. 
   390 We have only scratched the surface of Isabelle/HOL's set theory, which provides
   391 Hundreds of theorems are proved in theory \isa{Set} and its
   391 hundreds of theorems for your use.
   392 descendants.
       
   393 
   392 
   394 
   393 
   395 \subsection{Finiteness and Cardinality}
   394 \subsection{Finiteness and Cardinality}
   396 
   395 
   397 \index{sets!finite}%
   396 \index{sets!finite}%
  1068 \end{isabelle}
  1067 \end{isabelle}
  1069 A \textbf{bisimulation}\index{bisimulations} 
  1068 A \textbf{bisimulation}\index{bisimulations} 
  1070 is perhaps the best-known concept defined as a
  1069 is perhaps the best-known concept defined as a
  1071 greatest fixed point.  Exhibiting a bisimulation to prove the equality of
  1070 greatest fixed point.  Exhibiting a bisimulation to prove the equality of
  1072 two agents in a process algebra is an example of coinduction.
  1071 two agents in a process algebra is an example of coinduction.
  1073 The coinduction rule can be strengthened in various ways; see 
  1072 The coinduction rule can be strengthened in various ways.
  1074 theory \isa{Gfp} for details.  
       
  1075 \index{fixed points|)}
  1073 \index{fixed points|)}