11414
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\begin{theindex}
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\item \emph {$\forall \tmspace +\thinmuskip {.1667em}$}, \bold{3},
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\bold{189}
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\item \ttall, \bold{189}
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\item \emph {$\exists \tmspace +\thinmuskip {.1667em}$}, \bold{3},
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\bold{189}
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\item \texttt{?}, \hyperpage{5}, \bold{189}
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\item \emph {$\varepsilon $}, \bold{189}
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\item \isasymuniqex, \bold{3}, \bold{189}
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\item \ttuniquex, \bold{189}
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\item \emph {$\wedge $}, \bold{3}, \bold{189}
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\item {\texttt {\&}}, \bold{189}
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\item \texttt {=}, \bold{3}
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\item \emph {$\DOTSB \relbar \joinrel \rightarrow $}, \bold{3},
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\bold{189}
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\item \texttt {-->}, \bold{189}
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\item \emph {$\neg $}, \bold{3}, \bold{189}
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\item \verb$~$, \bold{189}
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\item \emph {$\not =$}, \bold{189}
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\item \verb$~=$, \bold{189}
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\item \emph {$\vee $}, \bold{3}, \bold{189}
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\item \ttor, \bold{189}
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\item \emph {$\circ $}, \bold{189}
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\item \emph {$\mid $}\nobreakspace {}\emph {$\mid $}, \bold{189}
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\item \texttt {*}, \bold{20, 21}, \bold{189}
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\item \texttt {+}, \bold{20, 21}
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\item \texttt {-}, \bold{20, 21}
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\item \emph {$\le $}, \bold{20, 21}, \bold{189}
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\item \texttt {<=}, \bold{189}
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\item \texttt {<}, \bold{20, 21}
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\item \texttt{[]}, \bold{7}
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\item \texttt{\#}, \bold{7}
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\item \texttt{\at}, \bold{8}, \hyperpage{189}
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\item \emph {$\in $}, \bold{189}
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\item \texttt {:}, \bold{189}
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\item \isasymnotin, \bold{189}
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\item \verb$~:$, \bold{189}
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\item \emph {$\subseteq $}, \bold{189}
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\item \emph {$\subset $}, \bold{189}
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\item \emph {$\cap $}, \bold{189}
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\item \emph {$\cup $}, \bold{189}
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\item \isasymInter, \bold{189}
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\item \isasymUnion, \bold{189}
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\item \isasyminverse, \bold{189}
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\item \verb$^-1$, \bold{189}
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\item \isactrlsup{\isacharasterisk}, \bold{189}
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\item \verb$^$\texttt{*}, \bold{189}
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\item \isasymAnd, \bold{10}, \bold{189}
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\item \ttAnd, \bold{189}
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\item \emph {$\equiv $}, \bold{23}, \bold{189}
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\item \texttt {==}, \bold{189}
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\item \emph {$\rightleftharpoons $}, \bold{23}, \bold{189}
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\item \emph {$\rightharpoonup $}, \bold{23}, \bold{189}
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\item \emph {$\leftharpoondown $}, \bold{23}, \bold{189}
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\item \emph {$\Rightarrow $}, \bold{3}, \bold{189}
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\item \texttt {=>}, \bold{189}
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\item \texttt {<=}, \bold{189}
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\item \emph {$\DOTSB \Relbar \joinrel \Rightarrow $}, \bold{189}
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\item \texttt {==>}, \bold{189}
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\item \emph {$\mathopen {[\mkern -3mu[}$}, \bold{10}, \bold{189}
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\item \ttlbr, \bold{189}
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\item \emph {$\mathclose {]\mkern -3mu]}$}, \bold{10}, \bold{189}
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\item \ttrbr, \bold{189}
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\item \emph {$\lambda $}, \bold{3}, \bold{189}
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\item \texttt {\%}, \bold{189}
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\item \texttt {,}, \bold{29}
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\item \texttt {;}, \bold{5}
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\item \emph {$\times $}, \bold{21}, \bold{189}
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\item \texttt {'a}, \bold{3}
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\item \texttt {()}, \bold{22}
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\item \texttt {::}, \bold{4}
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\item \isa {+} (tactical), \hyperpage{83}
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\item \isa {<*lex*>}, \see{lexicographic product}{1}
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\item \isa {?} (tactical), \hyperpage{83}
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\item \texttt{|} (tactical), \hyperpage{83}
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\indexspace
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\item \isa {0}, \bold{20}
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\item \texttt {0}, \bold{21}
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\indexspace
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\item abandon proof, \bold{11}
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\item abandon theory, \bold{14}
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\item \texttt {abs}, \bold{189}
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\item \isa {abs_mult} (theorem), \bold{135}
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\item \isa {add_2_eq_Suc} (theorem), \bold{133}
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\item \isa {add_2_eq_Suc'} (theorem), \bold{133}
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\item \isa {add_assoc} (theorem), \bold{134}
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\item \isa {add_commute} (theorem), \bold{134}
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\item \isa {add_left_commute} (theorem), \bold{134}
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\item \isa {add_mult_distrib} (theorem), \bold{133}
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\item \texttt {ALL}, \bold{189}
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\item \isa {All} (constant), \hyperpage{93}
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\item \isa {allE} (theorem), \bold{65}
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\item \isa {allI} (theorem), \bold{64}
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\item \isa {analz_Crypt_if} (theorem), \bold{186}
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\item \isa {analz_idem} (theorem), \bold{180}
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\item \isa {analz_mono} (theorem), \bold{180}
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\item \isa {analz_synth} (theorem), \bold{180}
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\item \isa {append_take_drop_id} (theorem), \bold{127}
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\item apply, \bold{13}
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\item \isa {arg_cong} (theorem), \bold{80}
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\item \isa {arith}, \bold{21}
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\item arithmetic, \hyperpage{20--21}, \hyperpage{31}
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\item \textsc {ascii} symbols, \bold{189}
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\item associative-commutative function, \hyperpage{158}
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\item \isa {assumption} (method), \hyperpage{53}
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\item assumptions
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\subitem renaming, \hyperpage{66--67}
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\subitem reusing, \hyperpage{67}
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\item \isa {auto}, \hyperpage{36}
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\item \isa {auto} (method), \hyperpage{76}
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\item \isa {axclass}, \hyperpage{144--150}
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\item axiom of choice, \hyperpage{70}
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\item axiomatic type class, \hyperpage{144--150}
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\indexspace
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122 |
\item \isacommand {back} (command), \hyperpage{62}
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\item \isa {Ball} (constant), \hyperpage{93}
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\item \isa {ballI} (theorem), \bold{92}
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\item \isa {best} (method), \hyperpage{75, 76}
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\item \isa {Bex} (constant), \hyperpage{93}
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\item \isa {bexE} (theorem), \bold{92}
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\item \isa {bexI} (theorem), \bold{92}
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\item \isa {bij_def} (theorem), \bold{94}
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\item bijections, \hyperpage{94}
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\item binomial coefficients, \hyperpage{93}
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\item bisimulation, \bold{100}
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\item \isa {blast} (method), \hyperpage{72--75}
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\item \isa {bool}, \hyperpage{2}, \bold{3}
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\item \isa {bspec} (theorem), \bold{92}
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\item \isacommand{by} (command), \hyperpage{57}
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\indexspace
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\item \isa {card} (constant), \hyperpage{93}
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\item \isa {card_Pow} (theorem), \bold{93}
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\item \isa {card_Un_Int} (theorem), \bold{93}
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\item cardinality, \hyperpage{93}
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\item \isa {case}, \bold{3}, \hyperpage{4}, \bold{16},
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\hyperpage{30, 31}
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\item case distinction, \bold{17}
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\item case splits, \bold{29}
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\item \isa {case_tac}, \bold{17}
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\item \isa {case_tac} (method), \hyperpage{85}
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\item \isa {clarify} (method), \hyperpage{74}, \hyperpage{76}
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\item \isa {clarsimp} (method), \hyperpage{75, 76}
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\item \isa {classical} (theorem), \bold{57}
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\item closure
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\subitem reflexive and transitive, \hyperpage{96--98}
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\item \isa {coinduct} (theorem), \bold{100}
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\item coinduction, \bold{100}
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\item \isa {Collect} (constant), \hyperpage{93}
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\item \isa {Collect_mem_eq} (theorem), \bold{91}
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\item \isa {comp_def} (theorem), \bold{96}
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\item \isa {comp_mono} (theorem), \bold{96}
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\item \isa {Compl_iff} (theorem), \bold{90}
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\item \isa {Compl_partition} (theorem), \bold{90}
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\item \isa {Compl_Un} (theorem), \bold{90}
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\item complement
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\subitem of a set, \hyperpage{89}
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\item composition
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\subitem of functions, \bold{94}
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\subitem of relations, \bold{96}
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\item congruence rules, \bold{157}
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\item \isa {conjE} (theorem), \bold{55}
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\item \isa {conjI} (theorem), \bold{52}
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\item \isa {Cons}, \bold{7}
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\item \isa {constdefs}, \bold{23}
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\item \isa {contrapos_nn} (theorem), \bold{57}
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\item \isa {contrapos_np} (theorem), \bold{57}
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\item \isa {contrapos_pn} (theorem), \bold{57}
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\item \isa {contrapos_pp} (theorem), \bold{57}
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\item contrapositives, \hyperpage{57}
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\item converse
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\subitem of a relation, \bold{96}
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\item \isa {converse_comp} (theorem), \bold{96}
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\item \isa {converse_iff} (theorem), \bold{96}
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\item CTL, \hyperpage{100--110}
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\indexspace
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\item \isa {datatype}, \hyperpage{7}, \hyperpage{36--42}
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\item \isa {defer}, \bold{14}
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\item \isacommand {defer} (command), \hyperpage{84}
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\item definition, \bold{23}
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\subitem unfolding, \bold{28}
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\item \isa {defs}, \bold{23}
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\item descriptions
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\subitem definite, \hyperpage{69}
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\subitem indefinite, \hyperpage{70}
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\item \isa {dest} (attribute), \hyperpage{86}
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\item destruction rules, \hyperpage{55}
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\item \isa {Diff_disjoint} (theorem), \bold{90}
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\item \isa {diff_mult_distrib} (theorem), \bold{133}
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\item difference
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\subitem of sets, \bold{90}
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\item \isa {disjCI} (theorem), \bold{58}
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\item \isa {disjE} (theorem), \bold{54}
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\item \isa {div}, \bold{20}
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\item \isa {div_le_mono} (theorem), \bold{133}
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\item \isa {div_mult1_eq} (theorem), \bold{133}
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\item \isa {div_mult2_eq} (theorem), \bold{133}
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\item \isa {div_mult_mult1} (theorem), \bold{133}
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\item divides relation, \bold{68}, \hyperpage{78}, \hyperpage{85--87}
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\item \isa {DIVISION_BY_ZERO_DIV} (theorem), \bold{134}
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\item \isa {DIVISION_BY_ZERO_MOD} (theorem), \bold{134}
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\item domain
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\subitem of a relation, \hyperpage{96}
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\item \isa {Domain_iff} (theorem), \bold{96}
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\item done, \bold{11}
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\item \isa {drule_tac} (method), \hyperpage{60}, \hyperpage{80}
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\item \isa {dvd_add} (theorem), \bold{79}, \bold{134}
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\item \isa {dvd_anti_sym} (theorem), \bold{134}
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\item \isa {dvd_def} (theorem), \bold{68}, \bold{78}, \bold{134}
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\item \isa {dvd_mod} (theorem), \bold{87}
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\item \isa {dvd_mod_imp_dvd} (theorem), \bold{86}
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\item \isa {dvd_refl} (theorem), \bold{79}
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\item \isa {dvd_trans} (theorem), \bold{87}
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\indexspace
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\item \isa {elim!} (attribute), \hyperpage{115}
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\item elimination rules, \hyperpage{53--54}
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\item \isa {Eps} (constant), \hyperpage{93}
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\item equality
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\subitem of functions, \bold{93}
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\subitem of sets, \bold{90}
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\item \isa {equalityE} (theorem), \bold{90}
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\item \isa {equalityI} (theorem), \bold{90}
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\item \isa {erule}, \hyperpage{54}
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\item \isa {erule_tac} (method), \hyperpage{60}
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\item Euclid's algorithm, \hyperpage{85--87}
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\item even numbers
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\subitem defining inductively, \hyperpage{111--115}
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\item \isa {even.cases} (theorem), \bold{114}
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\item \isa {even.induct} (theorem), \bold{112}
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\item \isa {even.step} (theorem), \bold{112}
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\item \isa {even.zero} (theorem), \bold{112}
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\item \texttt {EX}, \bold{189}
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\item \isa {Ex} (constant), \hyperpage{93}
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\item \isa {exE} (theorem), \bold{66}
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\item \isa {exI} (theorem), \bold{66}
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\item \isa {expand_fun_eq} (theorem), \bold{94}
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\item \isa {ext} (theorem), \bold{93}
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\item extensionality
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\subitem for functions, \bold{93, 94}
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\subitem for sets, \bold{90}
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\item \ttEXU, \bold{189}
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\indexspace
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\item \isa {False}, \bold{3}
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\item \isa {fast} (method), \hyperpage{75, 76}
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\item \isa {finite} (symbol), \hyperpage{93}
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\item \isa {Finites} (constant), \hyperpage{93}
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\item fixed points, \hyperpage{100}
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\item flag, \hyperpage{3, 4}, \hyperpage{31}
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\subitem (re)setting, \bold{3}
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\item \isa {force} (method), \hyperpage{75, 76}
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\item formula, \bold{3}
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\item forward proof, \hyperpage{76--82}
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\item \isa {frule} (method), \hyperpage{67}
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\item \isa {frule_tac} (method), \hyperpage{60}
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\item \isa {fst}, \bold{21}
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\item \isa {fun_upd_apply} (theorem), \bold{94}
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\item \isa {fun_upd_upd} (theorem), \bold{94}
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\item functions, \hyperpage{93--95}
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\indexspace
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276 |
\item \isa {gcd} (constant), \hyperpage{76--78}, \hyperpage{85--87}
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277 |
\item \isa {gcd_mult_distrib2} (theorem), \bold{77}
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278 |
\item generalizing for induction, \hyperpage{113}
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\item \isa {gfp_unfold} (theorem), \bold{100}
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280 |
\item Girard, Jean-Yves, \fnote{55}
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\item ground terms example, \hyperpage{119--124}
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\item \isa {gterm_Apply_elim} (theorem), \bold{123}
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\indexspace
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\item \isa {hd}, \bold{15}
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\item higher-order pattern, \bold{159}
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\item Hilbert's $\varepsilon$-operator, \hyperpage{69--71}
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\indexspace
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292 |
\item \isa {Id_def} (theorem), \bold{96}
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293 |
\item \isa {id_def} (theorem), \bold{94}
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294 |
\item identifier, \bold{4}
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\subitem qualified, \bold{2}
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\item identity function, \bold{94}
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297 |
\item identity relation, \bold{96}
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\item \isa {if}, \bold{3}, \hyperpage{4}
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\item \isa {iff} (attribute), \hyperpage{73, 74}, \hyperpage{86},
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300 |
\hyperpage{114}
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301 |
\item \isa {iffD1} (theorem), \bold{78}
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\item \isa {iffD2} (theorem), \bold{78}
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\item image
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304 |
\subitem under a function, \bold{95}
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305 |
\subitem under a relation, \bold{96}
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306 |
\item \isa {image_compose} (theorem), \bold{95}
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\item \isa {image_def} (theorem), \bold{95}
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308 |
\item \isa {Image_iff} (theorem), \bold{96}
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309 |
\item \isa {image_Int} (theorem), \bold{95}
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\item \isa {image_Un} (theorem), \bold{95}
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311 |
\item \isa {impI} (theorem), \bold{56}
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312 |
\item implication, \hyperpage{56--57}
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313 |
\item \isa {induct_tac}, \hyperpage{10}, \hyperpage{17},
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314 |
\hyperpage{50}, \hyperpage{172}
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315 |
\item induction, \hyperpage{168--175}
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\subitem recursion, \hyperpage{49--50}
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317 |
\subitem structural, \bold{17}
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318 |
\subitem well-founded, \hyperpage{99}
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|
319 |
\item \isacommand {inductive} (command), \hyperpage{111}
|
|
320 |
\item inductive definition, \hyperpage{111--129}
|
|
321 |
\subitem simultaneous, \hyperpage{125}
|
|
322 |
\item \isacommand {inductive\_cases} (command), \hyperpage{115},
|
|
323 |
\hyperpage{123}
|
|
324 |
\item \isa {infixr}, \bold{8}
|
|
325 |
\item \isa {inj_on_def} (theorem), \bold{94}
|
|
326 |
\item injections, \hyperpage{94}
|
|
327 |
\item inner syntax, \bold{9}
|
|
328 |
\item \isa {insert} (constant), \hyperpage{91}
|
|
329 |
\item \isa {insert} (method), \hyperpage{80--82}
|
|
330 |
\item \isa {insert_is_Un} (theorem), \bold{91}
|
|
331 |
\item instance, \bold{145}
|
|
332 |
\item \texttt {INT}, \bold{189}
|
|
333 |
\item \texttt {Int}, \bold{189}
|
|
334 |
\item \isa {INT_iff} (theorem), \bold{92}
|
|
335 |
\item \isa {IntD1} (theorem), \bold{89}
|
|
336 |
\item \isa {IntD2} (theorem), \bold{89}
|
|
337 |
\item \isa {INTER} (constant), \hyperpage{93}
|
|
338 |
\item \texttt {Inter}, \bold{189}
|
|
339 |
\item \isa {Inter_iff} (theorem), \bold{92}
|
|
340 |
\item intersection, \hyperpage{89}
|
|
341 |
\subitem indexed, \hyperpage{92}
|
|
342 |
\item \isa {IntI} (theorem), \bold{89}
|
|
343 |
\item \isa {intro} (method), \hyperpage{58}
|
|
344 |
\item \isa {intro!} (attribute), \hyperpage{112}
|
|
345 |
\item introduction rules, \hyperpage{52--53}
|
|
346 |
\item \isa {inv} (constant), \hyperpage{70}
|
|
347 |
\item \isa {inv_def} (theorem), \bold{70}
|
|
348 |
\item \isa {inv_f_f} (theorem), \bold{94}
|
|
349 |
\item \isa {inv_image_def} (theorem), \bold{99}
|
|
350 |
\item \isa {inv_inv_eq} (theorem), \bold{94}
|
|
351 |
\item inverse
|
|
352 |
\subitem of a function, \bold{94}
|
|
353 |
\subitem of a relation, \bold{96}
|
|
354 |
\item inverse image
|
|
355 |
\subitem of a function, \hyperpage{95}
|
|
356 |
\subitem of a relation, \hyperpage{98}
|
|
357 |
|
|
358 |
\indexspace
|
|
359 |
|
|
360 |
\item \isa {kill}, \bold{14}
|
|
361 |
|
|
362 |
\indexspace
|
|
363 |
|
|
364 |
\item \isa {le_less_trans} (theorem), \bold{171}
|
|
365 |
\item \isa {LEAST}, \bold{20}
|
|
366 |
\item least number operator, \hyperpage{69}
|
|
367 |
\item lemma, \hyperpage{11}
|
|
368 |
\item \isa {lemma}, \bold{11}
|
|
369 |
\item \isacommand {lemmas} (command), \hyperpage{77}, \hyperpage{86}
|
|
370 |
\item \isa {length}, \bold{15}
|
|
371 |
\item \isa {length_induct}, \bold{172}
|
|
372 |
\item \isa {less_than} (constant), \hyperpage{98}
|
|
373 |
\item \isa {less_than_iff} (theorem), \bold{98}
|
|
374 |
\item \isa {let}, \bold{3}, \hyperpage{4}, \hyperpage{29}
|
|
375 |
\item \isa {lex_prod_def} (theorem), \bold{99}
|
|
376 |
\item lexicographic product, \bold{99}, \hyperpage{160}
|
|
377 |
\item {\texttt{lfp}}
|
|
378 |
\subitem applications of, \see{CTL}{100}
|
|
379 |
\item \isa {lfp_induct} (theorem), \bold{100}
|
|
380 |
\item \isa {lfp_unfold} (theorem), \bold{100}
|
|
381 |
\item linear arithmetic, \bold{21}
|
|
382 |
\item \isa {list}, \hyperpage{2}, \bold{7}, \bold{15}
|
|
383 |
\item \isa {lists_Int_eq} (theorem), \bold{123}
|
|
384 |
\item \isa {lists_mono} (theorem), \bold{121}
|
|
385 |
|
|
386 |
\indexspace
|
|
387 |
|
|
388 |
\item \isa {Main}, \bold{2}
|
|
389 |
\item major premise, \bold{59}
|
|
390 |
\item \isa {max}, \bold{20, 21}
|
|
391 |
\item measure function, \bold{45}, \bold{98}
|
|
392 |
\item \isa {measure_def} (theorem), \bold{99}
|
|
393 |
\item \isa {mem_Collect_eq} (theorem), \bold{91}
|
|
394 |
\item meta-logic, \bold{64}
|
|
395 |
\item method, \bold{14}
|
|
396 |
\item \isa {min}, \bold{20, 21}
|
|
397 |
\item \isa {mod}, \bold{20}
|
|
398 |
\item \isa {mod_div_equality} (theorem), \bold{81}, \bold{133}
|
|
399 |
\item \isa {mod_if} (theorem), \bold{133}
|
|
400 |
\item \isa {mod_mult1_eq} (theorem), \bold{133}
|
|
401 |
\item \isa {mod_mult2_eq} (theorem), \bold{133}
|
|
402 |
\item \isa {mod_mult_distrib} (theorem), \bold{133}
|
|
403 |
\item \isa {mod_Suc} (theorem), \bold{80}
|
|
404 |
\item \emph{modus ponens}, \hyperpage{51}, \hyperpage{56}
|
|
405 |
\item \isa {mono_def} (theorem), \bold{100}
|
|
406 |
\item \isa {mono_Int} (theorem), \bold{123}
|
|
407 |
\item \isa {monoD} (theorem), \bold{100}
|
|
408 |
\item \isa {monoI} (theorem), \bold{100}
|
|
409 |
\item monotone functions, \bold{100}, \hyperpage{123}
|
|
410 |
\subitem and inductive definitions, \hyperpage{121--122}
|
|
411 |
\item \isa {mp} (theorem), \bold{56}
|
|
412 |
\item \isa {mult_commute} (theorem), \bold{61}
|
|
413 |
\item \isa {mult_le_mono} (theorem), \bold{133}
|
|
414 |
\item \isa {mult_le_mono1} (theorem), \bold{80}
|
|
415 |
\item \isa {mult_less_mono1} (theorem), \bold{133}
|
|
416 |
\item multiset ordering, \bold{99}
|
|
417 |
|
|
418 |
\indexspace
|
|
419 |
|
|
420 |
\item \isa {n_subsets} (theorem), \bold{93}
|
|
421 |
\item \isa {nat}, \hyperpage{2}, \bold{20}
|
|
422 |
\item \isa {nat_diff_split} (theorem), \bold{134}
|
|
423 |
\item natural deduction, \hyperpage{51--52}
|
|
424 |
\item \isa {neg_mod_bound} (theorem), \bold{135}
|
|
425 |
\item \isa {neg_mod_sign} (theorem), \bold{135}
|
|
426 |
\item negation, \hyperpage{57--59}
|
|
427 |
\item \isa {Nil}, \bold{7}
|
|
428 |
\item \isa {no_asm}, \bold{27}
|
|
429 |
\item \isa {no_asm_simp}, \bold{27}
|
|
430 |
\item \isa {no_asm_use}, \bold{28}
|
|
431 |
\item \isa {None}, \bold{22}
|
|
432 |
\item \isa {notE} (theorem), \bold{57}
|
|
433 |
\item \isa {notI} (theorem), \bold{57}
|
|
434 |
\item \isa {numeral_0_eq_0} (theorem), \bold{133}
|
|
435 |
\item \isa {numeral_1_eq_1} (theorem), \bold{133}
|
|
436 |
|
|
437 |
\indexspace
|
|
438 |
|
|
439 |
\item \isa {O} (symbol), \hyperpage{96}
|
|
440 |
\item \texttt {o}, \bold{189}
|
|
441 |
\item \isa {o_assoc} (theorem), \bold{94}
|
|
442 |
\item \isa {o_def} (theorem), \bold{94}
|
|
443 |
\item \isa {OF} (attribute), \hyperpage{78--79}
|
|
444 |
\item \isa {of} (attribute), \hyperpage{77}, \hyperpage{79}
|
|
445 |
\item \isa {oops}, \bold{11}
|
|
446 |
\item \isa {option}, \bold{22}
|
|
447 |
\item \isa {order_antisym} (theorem), \bold{69}
|
|
448 |
\item ordered rewriting, \bold{158}
|
|
449 |
\item outer syntax, \bold{9}
|
|
450 |
\item overloading, \hyperpage{144--146}
|
|
451 |
|
|
452 |
\indexspace
|
|
453 |
|
|
454 |
\item pair, \bold{21}, \hyperpage{137--140}
|
|
455 |
\item parent theory, \bold{2}
|
|
456 |
\item partial function, \hyperpage{164}
|
|
457 |
\item pattern, higher-order, \bold{159}
|
|
458 |
\item PDL, \hyperpage{102--105}
|
|
459 |
\item permutative rewrite rule, \bold{158}
|
|
460 |
\item \isa {pos_mod_bound} (theorem), \bold{135}
|
|
461 |
\item \isa {pos_mod_sign} (theorem), \bold{135}
|
|
462 |
\item \isa {pr}, \bold{14}
|
|
463 |
\item \isacommand {pr} (command), \hyperpage{83}
|
|
464 |
\item \isa {prefer}, \bold{14}
|
|
465 |
\item \isacommand {prefer} (command), \hyperpage{84}
|
|
466 |
\item primitive recursion, \bold{16}
|
|
467 |
\item \isa {primrec}, \hyperpage{8}, \bold{16}, \hyperpage{36--42}
|
|
468 |
\item product type, \see{pair}{1}
|
|
469 |
\item proof
|
|
470 |
\subitem abandon, \bold{11}
|
|
471 |
\item Proof General, \bold{5}
|
|
472 |
\item proofs
|
|
473 |
\subitem examples of failing, \hyperpage{71--72}
|
|
474 |
|
|
475 |
\indexspace
|
|
476 |
|
|
477 |
\item quantifiers
|
|
478 |
\subitem and inductive definitions, \hyperpage{119--121}
|
|
479 |
\subitem existential, \hyperpage{66}
|
|
480 |
\subitem for sets, \hyperpage{92}
|
|
481 |
\subitem instantiating, \hyperpage{68}
|
|
482 |
\subitem universal, \hyperpage{63--66}
|
|
483 |
|
|
484 |
\indexspace
|
|
485 |
|
|
486 |
\item \isa {r_into_rtrancl} (theorem), \bold{96}
|
|
487 |
\item \isa {r_into_trancl} (theorem), \bold{97}
|
|
488 |
\item \isa {R_O_Id} (theorem), \bold{96}
|
|
489 |
\item range
|
|
490 |
\subitem of a function, \hyperpage{95}
|
|
491 |
\subitem of a relation, \hyperpage{96}
|
|
492 |
\item \isa {range} (symbol), \hyperpage{95}
|
|
493 |
\item \isa {Range_iff} (theorem), \bold{96}
|
|
494 |
\item \isa {real_add_divide_distrib} (theorem), \bold{136}
|
|
495 |
\item \isa {real_dense} (theorem), \bold{136}
|
|
496 |
\item \isa {real_divide_divide1_eq} (theorem), \bold{136}
|
|
497 |
\item \isa {real_divide_divide2_eq} (theorem), \bold{136}
|
|
498 |
\item \isa {real_divide_minus_eq} (theorem), \bold{136}
|
|
499 |
\item \isa {real_minus_divide_eq} (theorem), \bold{136}
|
|
500 |
\item \isa {real_times_divide1_eq} (theorem), \bold{136}
|
|
501 |
\item \isa {real_times_divide2_eq} (theorem), \bold{136}
|
|
502 |
\item \isa {realpow_abs} (theorem), \bold{136}
|
|
503 |
\item \isa {recdef}, \hyperpage{45--50}, \hyperpage{160--168}
|
|
504 |
\item \isacommand {recdef} (command), \hyperpage{98}
|
|
505 |
\item \isa {recdef_cong}, \bold{164}
|
|
506 |
\item \isa {recdef_simp}, \bold{47}
|
|
507 |
\item \isa {recdef_wf}, \bold{162}
|
|
508 |
\item recursion
|
|
509 |
\subitem well-founded, \bold{161}
|
|
510 |
\item recursion induction, \hyperpage{49--50}
|
|
511 |
\item \isa {redo}, \bold{14}
|
|
512 |
\item relations, \hyperpage{95--98}
|
|
513 |
\subitem well-founded, \hyperpage{98--99}
|
|
514 |
\item \isa {relprime_dvd_mult} (theorem), \bold{78}
|
|
515 |
\item \isa {rename_tac} (method), \hyperpage{66--67}
|
|
516 |
\item \isa {rev}, \bold{8}
|
|
517 |
\item rewrite rule, \bold{26}
|
|
518 |
\subitem permutative, \bold{158}
|
|
519 |
\item rewriting, \bold{26}
|
|
520 |
\subitem ordered, \bold{158}
|
|
521 |
\item \isa {rotate_tac}, \bold{28}
|
|
522 |
\item \isa {rtrancl_idemp} (theorem), \bold{97}
|
|
523 |
\item \isa {rtrancl_induct} (theorem), \bold{97}
|
|
524 |
\item \isa {rtrancl_refl} (theorem), \bold{96}
|
|
525 |
\item \isa {rtrancl_trans} (theorem), \bold{96}
|
|
526 |
\item \isa {rtrancl_unfold} (theorem), \bold{96}
|
|
527 |
\item rule induction, \hyperpage{112--114}
|
|
528 |
\item rule inversion, \hyperpage{114--115}, \hyperpage{123--124}
|
|
529 |
\item \isa {rule_tac} (method), \hyperpage{60}
|
|
530 |
\subitem and renaming, \hyperpage{67}
|
|
531 |
|
|
532 |
\indexspace
|
|
533 |
|
|
534 |
\item \isa {safe} (method), \hyperpage{75, 76}
|
|
535 |
\item safe rules, \bold{73}
|
|
536 |
\item schematic variable, \bold{4}
|
|
537 |
\item \isa {set}, \hyperpage{2}
|
|
538 |
\item {\textit {set}} (type), \hyperpage{89}
|
|
539 |
\item set comprehensions, \hyperpage{91--92}
|
|
540 |
\item \isa {set_ext} (theorem), \bold{90}
|
|
541 |
\item sets, \hyperpage{89--93}
|
|
542 |
\subitem finite, \hyperpage{93}
|
|
543 |
\subitem notation for finite, \bold{91}
|
|
544 |
\item \isa {show_brackets}, \bold{4}
|
|
545 |
\item \isa {show_types}, \bold{3}
|
|
546 |
\item \texttt {show_types}, \hyperpage{14}
|
|
547 |
\item \isa {simp} (attribute), \bold{9}, \hyperpage{26}
|
|
548 |
\item \isa {simp} (method), \bold{26}
|
|
549 |
\item \isa {simp_all}, \hyperpage{26}, \hyperpage{36}
|
|
550 |
\item simplification, \hyperpage{25--32}, \hyperpage{157--160}
|
|
551 |
\subitem of let-expressions, \hyperpage{29}
|
|
552 |
\subitem ordered, \bold{158}
|
|
553 |
\subitem with definitions, \hyperpage{28}
|
|
554 |
\subitem with/of assumptions, \hyperpage{27}
|
|
555 |
\item simplification rule, \bold{26}, \hyperpage{159--160}
|
|
556 |
\item \isa {simplified} (attribute), \hyperpage{77}, \hyperpage{79}
|
|
557 |
\item simplifier, \bold{25}
|
|
558 |
\item \isa {size}, \bold{15}
|
|
559 |
\item \isa {snd}, \bold{21}
|
|
560 |
\item \isa {SOME} (symbol), \hyperpage{69}
|
|
561 |
\item \texttt {SOME}, \bold{189}
|
|
562 |
\item \isa {Some}, \bold{22}
|
|
563 |
\item \isa {some_equality} (theorem), \bold{69}
|
|
564 |
\item \isa {someI} (theorem), \bold{70}, \bold{75}
|
|
565 |
\item \isa {someI2} (theorem), \bold{70}
|
|
566 |
\item \isa {someI_ex} (theorem, \bold){71}
|
|
567 |
\item sort, \bold{150}
|
|
568 |
\item \isa {spec} (theorem), \bold{64}
|
|
569 |
\item \isa {split} (constant), \bold{137}
|
|
570 |
\item \isa {split} (method, attr.), \hyperpage{29--31}
|
|
571 |
\item split rule, \bold{30}
|
|
572 |
\item \isa {split_if}, \bold{30}
|
|
573 |
\item \isa {ssubst} (theorem), \bold{61}
|
|
574 |
\item structural induction, \bold{17}
|
|
575 |
\item \isa {subgoal_tac} (method), \hyperpage{81, 82}
|
|
576 |
\item subset relation, \bold{90}
|
|
577 |
\item \isa {subsetD} (theorem), \bold{90}
|
|
578 |
\item \isa {subsetI} (theorem), \bold{90}
|
|
579 |
\item \isa {subst} (method), \hyperpage{61}
|
|
580 |
\item substitution, \hyperpage{61--63}
|
|
581 |
\item \isa {Suc}, \bold{20}
|
|
582 |
\item \isa {Suc_leI} (theorem), \bold{171}
|
|
583 |
\item \isa {Suc_Suc_cases} (theorem), \bold{115}
|
|
584 |
\item \isa {surj_def} (theorem), \bold{94}
|
|
585 |
\item \isa {surj_f_inv_f} (theorem), \bold{94}
|
|
586 |
\item surjections, \hyperpage{94}
|
|
587 |
\item \isa {sym} (theorem), \bold{77}
|
|
588 |
\item syntax translation, \bold{23}
|
|
589 |
|
|
590 |
\indexspace
|
|
591 |
|
|
592 |
\item tactic, \bold{10}
|
|
593 |
\item tacticals, \hyperpage{82--83}
|
|
594 |
\item term, \bold{3}
|
|
595 |
\item \isa {term}, \bold{14}
|
|
596 |
\item term rewriting, \bold{26}
|
|
597 |
\item termination, \see{total function}{1}
|
|
598 |
\item \isa {THEN} (attribute), \bold{77}, \hyperpage{79},
|
|
599 |
\hyperpage{86}
|
|
600 |
\item theorem, \hyperpage{11}
|
|
601 |
\item \isa {theorem}, \bold{9}, \hyperpage{11}
|
|
602 |
\item theory, \bold{2}
|
|
603 |
\subitem abandon, \bold{14}
|
|
604 |
\item theory file, \bold{2}
|
|
605 |
\item \isa {thm}, \bold{14}
|
|
606 |
\item \isa {tl}, \bold{15}
|
|
607 |
\item total function, \hyperpage{9}
|
|
608 |
\item \isa {trace_simp}, \bold{31}
|
|
609 |
\item tracing the simplifier, \bold{31}
|
|
610 |
\item \isa {trancl_converse} (theorem), \bold{97}
|
|
611 |
\item \isa {trancl_trans} (theorem), \bold{97}
|
|
612 |
\item \isa {translations}, \bold{23}
|
|
613 |
\item \isa {True}, \bold{3}
|
|
614 |
\item tuple, \see{pair}{1}
|
|
615 |
\item \isa {typ}, \bold{14}
|
|
616 |
\item type, \bold{2}
|
|
617 |
\item type constraint, \bold{4}
|
|
618 |
\item type declaration, \bold{150}
|
|
619 |
\item type definition, \bold{151}
|
|
620 |
\item type inference, \bold{3}
|
|
621 |
\item type synonym, \bold{22}
|
|
622 |
\item type variable, \bold{3}
|
|
623 |
\item \isa {typedecl}, \bold{151}
|
|
624 |
\item \isa {typedef}, \bold{151}
|
|
625 |
\item \isa {types}, \bold{22}
|
|
626 |
|
|
627 |
\indexspace
|
|
628 |
|
|
629 |
\item \texttt {UN}, \bold{189}
|
|
630 |
\item \texttt {Un}, \bold{189}
|
|
631 |
\item \isa {UN_E} (theorem), \bold{92}
|
|
632 |
\item \isa {UN_I} (theorem), \bold{92}
|
|
633 |
\item \isa {UN_iff} (theorem), \bold{92}
|
|
634 |
\item \isa {Un_subset_iff} (theorem), \bold{90}
|
|
635 |
\item underdefined function, \hyperpage{165}
|
|
636 |
\item \isa {undo}, \bold{14}
|
|
637 |
\item \isa {unfold}, \bold{28}
|
|
638 |
\item unification, \hyperpage{60--63}
|
|
639 |
\item \isa {UNION} (constant), \hyperpage{93}
|
|
640 |
\item \texttt {Union}, \bold{189}
|
|
641 |
\item union
|
|
642 |
\subitem indexed, \hyperpage{92}
|
|
643 |
\item \isa {Union_iff} (theorem), \bold{92}
|
|
644 |
\item \isa {unit}, \bold{22}
|
|
645 |
\item unknown, \bold{4}
|
|
646 |
\item unknowns, \bold{52}
|
|
647 |
\item unsafe rules, \bold{73}
|
|
648 |
\item updating a function, \bold{93}
|
|
649 |
|
|
650 |
\indexspace
|
|
651 |
|
|
652 |
\item variable, \bold{4}
|
|
653 |
\subitem schematic, \bold{4}
|
|
654 |
\subitem type, \bold{3}
|
|
655 |
\item \isa {vimage_Compl} (theorem), \bold{95}
|
|
656 |
\item \isa {vimage_def} (theorem), \bold{95}
|
|
657 |
|
|
658 |
\indexspace
|
|
659 |
|
|
660 |
\item \isa {wf_induct} (theorem), \bold{99}
|
|
661 |
\item \isa {wf_inv_image} (theorem), \bold{99}
|
|
662 |
\item \isa {wf_less_than} (theorem), \bold{98}
|
|
663 |
\item \isa {wf_lex_prod} (theorem), \bold{99}
|
|
664 |
\item \isa {wf_measure} (theorem), \bold{99}
|
|
665 |
\item \isa {while}, \bold{167}
|
|
666 |
|
|
667 |
\indexspace
|
|
668 |
|
|
669 |
\item \isa {zdiv_zadd1_eq} (theorem), \bold{135}
|
|
670 |
\item \isa {zdiv_zmult1_eq} (theorem), \bold{135}
|
|
671 |
\item \isa {zdiv_zmult2_eq} (theorem), \bold{135}
|
|
672 |
\item \isa {zmod_zadd1_eq} (theorem), \bold{135}
|
|
673 |
\item \isa {zmod_zmult1_eq} (theorem), \bold{135}
|
|
674 |
\item \isa {zmod_zmult2_eq} (theorem), \bold{135}
|
|
675 |
|
|
676 |
\end{theindex}
|