\chapter{Isabelle/Isar Quick Reference}\label{ap:refcard}
\section{Proof commands}
\subsection{Primitives and basic syntax}
\begin{tabular}{ll}
$\FIX{x}$ & augment context by $\All x \Box$ \\
$\ASSUME{a}{\phi}$ & augment context by $\phi \Imp \Box$ \\
$\THEN$ & indicate forward chaining \\
$\HAVE{a}{\phi}$ & prove local result \\
$\SHOW{a}{\phi}$ & prove local result, establishing some goal \\
$\PROOF{m@1}~\dots~\QED{m@2}$ & apply proof methods \\
$\BG~\dots~\EN$ & declare explicit blocks \\
$\isarcmd{next}$ & switch implicit blocks \\
$\NOTE{a}{a@1\;\dots\;a@n}$ & reconsider facts \\
$\LET{p = t}$ & \text{abbreviate terms by higher-order matching} \\
\end{tabular}
\begin{matharray}{rcl}
theory{\dsh}stmt & = & \THEOREM{name}{prop} ~proof \\
& \Or & \LEMMA{name}{prop}~proof \\
& \Or & \TYPES~\dots \Or \CONSTS~\dots \Or \DEFS~\dots \Or \dots \\[1ex]
proof & = & \PROOF{method}~stmt^*~\QED{method} \\[1ex]
stmt & = & \BG~stmt^*~\EN \\
& \Or & \isarcmd{next} \\
& \Or & \NOTE{name}{name^+} \\
& \Or & \LET{term = term} \\[0.5ex]
& \Or & \FIX{var^+} \\
& \Or & \ASSUME{name}{prop^+}\\
& \Or & \THEN~goal{\dsh}stmt \\
& \Or & goal{\dsh}stmt \\
goal{\dsh}stmt & = & \HAVE{name}{prop}~proof \\
& \Or & \SHOW{name}{prop}~proof \\
\end{matharray}
\subsection{Abbreviations and synonyms}
\begin{matharray}{rcl}
\BYY{m@1}{m@2} & \equiv & \PROOF{m@1}~\QED{m@2} \\
\DDOT & \equiv & \BY{rule} \\
\DOT & \equiv & \BY{this} \\
\HENCENAME & \equiv & \THEN~\HAVENAME \\
\THUSNAME & \equiv & \THEN~\SHOWNAME \\
\FROM{a@1\;\dots\;a@n} & \equiv & \NOTE{this}{a@1\;\dots\;a@n}~\THEN \\
\WITH{a@1\;\dots\;a@n} & \equiv & \FROM{a@1\;\dots\;a@n~this} \\[1ex]
\FROM{this} & \equiv & \THEN \\
\FROM{this}~\HAVENAME & \equiv & \HENCENAME \\
\FROM{this}~\SHOWNAME & \equiv & \THUSNAME \\
\end{matharray}
\subsection{Derived elements}
\begin{matharray}{rcl}
\ALSO@0 & \approx & \NOTE{calculation}{this} \\
\ALSO@{n+1} & \approx & \NOTE{calculation}{trans~[OF~calculation~this]} \\
\FINALLY & \approx & \ALSO~\FROM{calculation} \\
\PRESUME{a}{\phi} & \approx & \ASSUME{a}{\phi} \\
\DEF{a}{x \equiv t} & \approx & \FIX{x}~\ASSUME{a}{x \equiv t} \\
\isarcmd{sorry} & \approx & \BY{cheating} \\
\end{matharray}
\subsection{Diagnostic commands}
\begin{matharray}{ll}
\isarcmd{thm}~a@1\;\dots\;a@n & \text{print theorems} \\
\isarcmd{term}~t & \text{print term} \\
\isarcmd{prop}~\phi & \text{print meta-level proposition} \\
\isarcmd{typ}~\tau & \text{print meta-level type} \\
\end{matharray}
\section{Proof methods}
\begin{tabular}{ll}
\multicolumn{2}{l}{\textbf{Single steps (forward-chaining facts)}} \\[0.5ex]
$assumption$ & apply some assumption \\
$this$ & apply current facts \\
$rule~a@1\;\dots\;a@n$ & apply some rule \\
$rule$ & apply standard rule (default for $\PROOFNAME$) \\
$induct~x$ & apply induction rule \\
$contradiction$ & apply $\neg{}$ elimination rule (any order) \\[2ex]
\multicolumn{2}{l}{\textbf{Repeated steps (inserting facts)}} \\[0.5ex]
$-$ & \text{no rules} \\
$intro~a@1\;\dots\;a@n$ & \text{introduction rules} \\
$elim~a@1\;\dots\;a@n$ & \text{elimination rules} \\
$unfold~a@1\;\dots\;a@n$ & \text{definitions} \\[2ex]
\multicolumn{2}{l}{\textbf{Automated proof tools (inserting facts, or even prems!)}} \\[0.5ex]
$simp$ & Simplifier \\
$blast$, $fast$ & Classical Reasoner \\
$force$, $auto$ & Simplifier + Classical Reasoner \\
$arith$ & Arithmetic procedure \\
\end{tabular}
\section{Attributes}
\begin{tabular}{ll}
\multicolumn{2}{l}{\textbf{Modify rules}} \\[0.5ex]
$OF~a@1\;\dots\;a@n$ & apply rule to facts (skipping ``$_$'') \\
$of~t@1\;\dots\;t@n$ & apply rule to terms (skipping ``$_$'') \\
$RS~b$ & resolve fact with rule \\
$standard$ & put into standard result form \\
$rulify$ & put into object-rule form \\
$elimify$ & put destruction rule into elimination form \\[1ex]
\multicolumn{2}{l}{\textbf{Modify context}} \\[0.5ex]
$simp$ & declare Simplifier rules \\
$intro$, $elim$, $dest$ & declare Classical Reasoner rules (also ``$!$'' or ``$!!$'') \\
$iff$ & declare Simplifier + Classical Reasoner rules \\
$trans$ & declare calculational rules (general transitivity) \\
\end{tabular}
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