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\begin{isabellebody}%
\def\isabellecontext{Quick{\isaliteral{5F}{\isacharunderscore}}Reference}%
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\isadelimtheory
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\endisadelimtheory
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\isatagtheory
\isacommand{theory}\isamarkupfalse%
\ Quick{\isaliteral{5F}{\isacharunderscore}}Reference\isanewline
\isakeyword{imports}\ Main\isanewline
\isakeyword{begin}%
\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
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\isamarkupchapter{Isabelle/Isar quick reference \label{ap:refcard}%
}
\isamarkuptrue%
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\isamarkupsection{Proof commands%
}
\isamarkuptrue%
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\isamarkupsubsection{Primitives and basic syntax%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
\begin{tabular}{ll}
    \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x} & augment context by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C626F783E}{\isasymbox}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & augment context by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C626F783E}{\isasymbox}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} & indicate forward chaining of facts \\
    \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & prove local result \\
    \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & prove local result, refining some goal \\
    \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{a} & indicate use of additional facts \\
    \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{a} & unfold definitional equations \\
    \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\dots~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} & indicate proof structure and refinements \\
    \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}} & indicate explicit blocks \\
    \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} & switch blocks \\
    \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{22}{\isachardoublequote}}} & reconsider facts \\
    \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}p\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequote}}} & abbreviate terms by higher-order matching \\
    \hyperlink{command.write}{\mbox{\isa{\isacommand{write}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ \ {\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & declare local mixfix syntax \\
  \end{tabular}

  \medskip

  \begin{tabular}{rcl}
    \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{22}{\isachardoublequote}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}prfx\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}\ stmt\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}prfx\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}} \\[0.5ex]
    \isa{prfx} & = & \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{method} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}facts{\isaliteral{22}{\isachardoublequote}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}facts{\isaliteral{22}{\isachardoublequote}}} \\
    \isa{stmt} & = & \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}stmt\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ facts{\isaliteral{22}{\isachardoublequote}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}term\ {\isaliteral{3D}{\isacharequal}}\ term{\isaliteral{22}{\isachardoublequote}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.write}{\mbox{\isa{\isacommand{write}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{28}{\isacharparenleft}}mixfix{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}var\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props{\isaliteral{22}{\isachardoublequote}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}~\isa{goal} \\
    \isa{goal} & = & \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props\ proof{\isaliteral{22}{\isachardoublequote}}} \\
    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props\ proof{\isaliteral{22}{\isachardoublequote}}} \\
  \end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsubsection{Abbreviations and synonyms%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
\begin{tabular}{rcl}
    \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{rule} \\
    \hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{this} \\
    \hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} \\
    \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} \\
    \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{a} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{a}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} \\
    \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{a} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ this{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
    \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} \\
    \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}} \\
    \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} \\
  \end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsubsection{Derived elements%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
\begin{tabular}{rcl}
    \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ this{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{2B}{\isacharplus}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ trans\ {\isaliteral{5B}{\isacharbrackleft}}OF\ calculation\ this{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\[0.5ex]
    \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ calculation\ this{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\[0.5ex]
    \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
      \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{cheating} \\
  \end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsubsection{Diagnostic commands%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
\begin{tabular}{ll}
    \hyperlink{command.pr}{\mbox{\isa{\isacommand{pr}}}} & print current state \\
    \hyperlink{command.thm}{\mbox{\isa{\isacommand{thm}}}}~\isa{a} & print fact \\
    \hyperlink{command.prop}{\mbox{\isa{\isacommand{prop}}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} & print proposition \\
    \hyperlink{command.term}{\mbox{\isa{\isacommand{term}}}}~\isa{t} & print term \\
    \hyperlink{command.typ}{\mbox{\isa{\isacommand{typ}}}}~\isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} & print type \\
  \end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsection{Proof methods%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
\begin{tabular}{ll}
    \multicolumn{2}{l}{\textbf{Single steps (forward-chaining facts)}} \\[0.5ex]
    \hyperlink{method.assumption}{\mbox{\isa{assumption}}} & apply some assumption \\
    \hyperlink{method.this}{\mbox{\isa{this}}} & apply current facts \\
    \hyperlink{method.rule}{\mbox{\isa{rule}}}~\isa{a} & apply some rule  \\
    \hyperlink{method.rule}{\mbox{\isa{rule}}} & apply standard rule (default for \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}) \\
    \hyperlink{method.contradiction}{\mbox{\isa{contradiction}}} & apply \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{22}{\isachardoublequote}}} elimination rule (any order) \\
    \hyperlink{method.cases}{\mbox{\isa{cases}}}~\isa{t} & case analysis (provides cases) \\
    \hyperlink{method.induct}{\mbox{\isa{induct}}}~\isa{x} & proof by induction (provides cases) \\[2ex]

    \multicolumn{2}{l}{\textbf{Repeated steps (inserting facts)}} \\[0.5ex]
    \hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}} & no rules \\
    \hyperlink{method.intro}{\mbox{\isa{intro}}}~\isa{a} & introduction rules \\
    \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}} & class introduction rules \\
    \hyperlink{method.elim}{\mbox{\isa{elim}}}~\isa{a} & elimination rules \\
    \hyperlink{method.unfold}{\mbox{\isa{unfold}}}~\isa{a} & definitional rewrite rules \\[2ex]

    \multicolumn{2}{l}{\textbf{Automated proof tools (inserting facts)}} \\[0.5ex]
    \hyperlink{method.iprover}{\mbox{\isa{iprover}}} & intuitionistic proof search \\
    \hyperlink{method.blast}{\mbox{\isa{blast}}}, \hyperlink{method.fast}{\mbox{\isa{fast}}} & Classical Reasoner \\
    \hyperlink{method.simp}{\mbox{\isa{simp}}}, \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} & Simplifier (+ Splitter) \\
    \hyperlink{method.auto}{\mbox{\isa{auto}}}, \hyperlink{method.force}{\mbox{\isa{force}}} & Simplifier + Classical Reasoner \\
    \hyperlink{method.arith}{\mbox{\isa{arith}}} & Arithmetic procedures \\
  \end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsection{Attributes%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
\begin{tabular}{ll}
    \multicolumn{2}{l}{\textbf{Operations}} \\[0.5ex]
    \hyperlink{attribute.OF}{\mbox{\isa{OF}}}~\isa{a} & rule resolved with facts (skipping ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'') \\
    \hyperlink{attribute.of}{\mbox{\isa{of}}}~\isa{t} & rule instantiated with terms (skipping ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'') \\
    \hyperlink{attribute.where}{\mbox{\isa{where}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequote}}} & rule instantiated with terms, by variable name \\
    \hyperlink{attribute.symmetric}{\mbox{\isa{symmetric}}} & resolution with symmetry rule \\
    \hyperlink{attribute.THEN}{\mbox{\isa{THEN}}}~\isa{b} & resolution with another rule \\
    \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}} & result put into standard rule format \\
    \hyperlink{attribute.elim-format}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}format}}} & destruct rule turned into elimination rule format \\[1ex]

    \multicolumn{2}{l}{\textbf{Declarations}} \\[0.5ex]
    \hyperlink{attribute.simp}{\mbox{\isa{simp}}} & Simplifier rule \\
    \hyperlink{attribute.intro}{\mbox{\isa{intro}}}, \hyperlink{attribute.elim}{\mbox{\isa{elim}}}, \hyperlink{attribute.dest}{\mbox{\isa{dest}}} & Pure or Classical Reasoner rule \\
    \hyperlink{attribute.iff}{\mbox{\isa{iff}}} & Simplifier + Classical Reasoner rule \\
    \hyperlink{attribute.split}{\mbox{\isa{split}}} & case split rule \\
    \hyperlink{attribute.trans}{\mbox{\isa{trans}}} & transitivity rule \\
    \hyperlink{attribute.sym}{\mbox{\isa{sym}}} & symmetry rule \\
  \end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsection{Rule declarations and methods%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
\begin{tabular}{l|lllll}
      & \hyperlink{method.rule}{\mbox{\isa{rule}}} & \hyperlink{method.iprover}{\mbox{\isa{iprover}}} & \hyperlink{method.blast}{\mbox{\isa{blast}}} & \hyperlink{method.simp}{\mbox{\isa{simp}}} & \hyperlink{method.auto}{\mbox{\isa{auto}}} \\
      &                &                   & \hyperlink{method.fast}{\mbox{\isa{fast}}} & \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} & \hyperlink{method.force}{\mbox{\isa{force}}} \\
    \hline
    \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}elim}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}} \hyperlink{attribute.Pure.intro}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}
      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}elim}}} \hyperlink{attribute.Pure.intro}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}intro}}}
      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.elim}{\mbox{\isa{elim}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}} \hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}
      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}    &                    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}          &                     & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.elim}{\mbox{\isa{elim}}} \hyperlink{attribute.intro}{\mbox{\isa{intro}}}
      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}    &                    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}          &                     & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.iff}{\mbox{\isa{iff}}}
      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}    &                    & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}          & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}         & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.iff}{\mbox{\isa{iff}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}
      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.elim}{\mbox{\isa{elim}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}
      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.simp}{\mbox{\isa{simp}}}
      &                &                    &                      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}         & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.cong}{\mbox{\isa{cong}}}
      &                &                    &                      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}         & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
    \hyperlink{attribute.split}{\mbox{\isa{split}}}
      &                &                    &                      & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}}         & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
  \end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsection{Emulating tactic scripts%
}
\isamarkuptrue%
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\isamarkupsubsection{Commands%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
\begin{tabular}{ll}
    \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{m} & apply proof method at initial position \\
    \hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isaliteral{5F}{\isacharunderscore}}end}}}}~\isa{m} & apply proof method near terminal position \\
    \hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}} & complete proof \\
    \hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}}~\isa{n} & move subgoal to end \\
    \hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}}~\isa{n} & move subgoal to beginning \\
    \hyperlink{command.back}{\mbox{\isa{\isacommand{back}}}} & backtrack last command \\
  \end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsubsection{Methods%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
\begin{tabular}{ll}
    \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & resolution (with instantiation) \\
    \hyperlink{method.erule-tac}{\mbox{\isa{erule{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & elim-resolution (with instantiation) \\
    \hyperlink{method.drule-tac}{\mbox{\isa{drule{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & destruct-resolution (with instantiation) \\
    \hyperlink{method.frule-tac}{\mbox{\isa{frule{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & forward-resolution (with instantiation) \\
    \hyperlink{method.cut-tac}{\mbox{\isa{cut{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & insert facts (with instantiation) \\
    \hyperlink{method.thin-tac}{\mbox{\isa{thin{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} & delete assumptions \\
    \hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} & new claims \\
    \hyperlink{method.rename-tac}{\mbox{\isa{rename{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{x} & rename innermost goal parameters \\
    \hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{n} & rotate assumptions of goal \\
    \hyperlink{method.tactic}{\mbox{\isa{tactic}}}~\isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} & arbitrary ML tactic \\
    \hyperlink{method.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{t} & exhaustion (datatypes) \\
    \hyperlink{method.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{x} & induction (datatypes) \\
    \hyperlink{method.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}}~\isa{t} & exhaustion + simplification (inductive predicates) \\
  \end{tabular}%
\end{isamarkuptext}%
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\isadelimtheory
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\endisadelimtheory
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\isatagtheory
\isacommand{end}\isamarkupfalse%
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\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
\isanewline
\end{isabellebody}%
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