equal
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inserted
replaced
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. |
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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|)} |