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\begin{isabellebody}%
\def\isabellecontext{Public}%
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\isadelimtheory
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\endisadelimtheory
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\isatagtheory
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\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
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\begin{isamarkuptext}%
The function
\isa{pubK} maps agents to their public keys.  The function
\isa{priK} maps agents to their private keys.  It is merely
an abbreviation (cf.\ \S\ref{sec:abbreviations}) defined in terms of
\isa{invKey} and \isa{pubK}.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{consts}\isamarkupfalse%
\ pubK\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}agent\ {\isasymRightarrow}\ key{\isachardoublequoteclose}\isanewline
\isacommand{abbreviation}\isamarkupfalse%
\ priK\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}agent\ {\isasymRightarrow}\ key{\isachardoublequoteclose}\isanewline
\isakeyword{where}\ {\isachardoublequoteopen}priK\ x\ \ {\isasymequiv}\ \ invKey{\isacharparenleft}pubK\ x{\isacharparenright}{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent
The set \isa{bad} consists of those agents whose private keys are known to
the spy.

Two axioms are asserted about the public-key cryptosystem. 
No two agents have the same public key, and no private key equals
any public key.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{axioms}\isamarkupfalse%
\isanewline
\ \ inj{\isacharunderscore}pubK{\isacharcolon}\ \ \ \ \ \ \ \ {\isachardoublequoteopen}inj\ pubK{\isachardoublequoteclose}\isanewline
\ \ priK{\isacharunderscore}neq{\isacharunderscore}pubK{\isacharcolon}\ \ \ {\isachardoublequoteopen}priK\ A\ {\isasymnoteq}\ pubK\ B{\isachardoublequoteclose}%
\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimproof
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\endisadelimproof
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\isatagproof
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\endisatagproof
{\isafoldproof}%
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\isadelimproof
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\endisadelimproof
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\isadelimML
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\endisadelimML
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\isatagML
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\endisatagML
{\isafoldML}%
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\isadelimML
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\endisadelimML
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\isadelimtheory
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\endisadelimtheory
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\isatagtheory
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\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
\end{isabellebody}%
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