\begin{theindex}
\item \emph {$\forall \tmspace +\thinmuskip {.1667em}$}, \bold{189}
\item \isasymforall, \bold{3}
\item \ttall, \bold{189}
\item \emph {$\exists \tmspace +\thinmuskip {.1667em}$}, \bold{189}
\item \isasymexists, \bold{3}
\item \texttt{?}, \hyperpage{5}, \bold{189}
\item \emph {$\varepsilon $}, \bold{189}
\item \isasymuniqex, \bold{3}, \bold{189}
\item \ttuniquex, \bold{189}
\item \emph {$\wedge $}, \bold{189}
\item \isasymand, \bold{3}
\item {\texttt {\&}}, \bold{189}
\item \texttt {=}, \bold{3}
\item \emph {$\DOTSB \relbar \joinrel \rightarrow $}, \bold{189}
\item \isasymimp, \bold{3}
\item \texttt {-->}, \bold{189}
\item \emph {$\neg $}, \bold{189}
\item \isasymnot, \bold{3}
\item \verb$~$, \bold{189}
\item \emph {$\not =$}, \bold{189}
\item \verb$~=$, \bold{189}
\item \emph {$\vee $}, \bold{189}
\item \isasymor, \bold{3}
\item \ttor, \bold{189}
\item \emph {$\circ $}, \bold{189}
\item \emph {$\mid $}\nobreakspace {}\emph {$\mid $}, \bold{189}
\item \texttt {*}, \bold{20, 21}, \bold{189}
\item \texttt {+}, \bold{20, 21}
\item \texttt {-}, \bold{20, 21}
\item \emph {$\le $}, \bold{20, 21}, \bold{189}
\item \texttt {<=}, \bold{189}
\item \texttt {<}, \bold{20, 21}
\item \texttt{[]}, \bold{7}
\item \texttt{\#}, \bold{7}
\item \texttt{\at}, \bold{8}, \hyperpage{189}
\item \emph {$\in $}, \bold{189}
\item \texttt {:}, \bold{189}
\item \isasymnotin, \bold{189}
\item \verb$~:$, \bold{189}
\item \emph {$\subseteq $}, \bold{189}
\item \emph {$\subset $}, \bold{189}
\item \emph {$\cap $}, \bold{189}
\item \emph {$\cup $}, \bold{189}
\item \isasymInter, \bold{189}
\item \isasymUnion, \bold{189}
\item \isasyminverse, \bold{189}
\item \verb$^-1$, \bold{189}
\item \isactrlsup{\isacharasterisk}, \bold{189}
\item \verb$^$\texttt{*}, \bold{189}
\item \isasymAnd, \bold{10}, \bold{189}
\item \ttAnd, \bold{189}
\item \emph {$\equiv $}, \bold{23}, \bold{189}
\item \texttt {==}, \bold{189}
\item \emph {$\rightleftharpoons $}, \bold{24}, \bold{189}
\item \emph {$\rightharpoonup $}, \bold{24}, \bold{189}
\item \emph {$\leftharpoondown $}, \bold{24}, \bold{189}
\item \emph {$\Rightarrow $}, \bold{3}, \bold{189}
\item \texttt {=>}, \bold{189}
\item \texttt {<=}, \bold{189}
\item \emph {$\DOTSB \Relbar \joinrel \Rightarrow $}, \bold{189}
\item \texttt {==>}, \bold{189}
\item \emph {$\mathopen {[\mkern -3mu[}$}, \bold{10}, \bold{189}
\item \ttlbr, \bold{189}
\item \emph {$\mathclose {]\mkern -3mu]}$}, \bold{10}, \bold{189}
\item \ttrbr, \bold{189}
\item \emph {$\lambda $}, \bold{3}, \bold{189}
\item \texttt {\%}, \bold{189}
\item \texttt {,}, \bold{29}
\item \texttt {;}, \bold{5}
\item \emph {$\times $}, \bold{21}, \bold{189}
\item \texttt {'a}, \bold{3}
\item \texttt {()}, \bold{22}
\item \texttt {::}, \bold{4}
\item \isa {+} (tactical), \hyperpage{83}
\item \isa {<*lex*>}, \see{lexicographic product}{1}
\item \isa {?} (tactical), \hyperpage{83}
\item \texttt{|} (tactical), \hyperpage{83}
\indexspace
\item \isa {0} (constant), \hyperpage{20, 21}, \hyperpage{133}
\item \isa {1} (symbol), \hyperpage{133}
\item \isa {2} (symbol), \hyperpage{133}
\indexspace
\item abandoning a proof, \bold{11}
\item abandoning a theory, \bold{14}
\item \isa {abs} (constant), \hyperpage{135}
\item \texttt {abs}, \bold{189}
\item absolute value, \hyperpage{135}
\item \isa {add_assoc} (theorem), \bold{134}
\item \isa {add_commute} (theorem), \bold{134}
\item \isa {add_mult_distrib} (theorem), \bold{133}
\item \texttt {ALL}, \bold{189}
\item \isa {All} (constant), \hyperpage{93}
\item \isa {allE} (theorem), \bold{65}
\item \isa {allI} (theorem), \bold{64}
\item \isacommand {apply} (command), \hyperpage{13}
\item \isa {arg_cong} (theorem), \bold{80}
\item \isa {arith} (method), \hyperpage{21}, \hyperpage{131}
\item \textsc {ascii} symbols, \bold{189}
\item associative-commutative function, \hyperpage{158}
\item \isa {assumption} (method), \hyperpage{53}
\item assumptions
\subitem renaming, \hyperpage{66--67}
\subitem reusing, \hyperpage{67}
\item \isa {auto} (method), \hyperpage{36}, \hyperpage{76}
\item \isa {axclass}, \hyperpage{144--150}
\item axiom of choice, \hyperpage{70}
\item axiomatic type classes, \hyperpage{144--150}
\indexspace
\item \isacommand {back} (command), \hyperpage{62}
\item \isa {Ball} (constant), \hyperpage{93}
\item \isa {ballI} (theorem), \bold{92}
\item \isa {best} (method), \hyperpage{75, 76}
\item \isa {Bex} (constant), \hyperpage{93}
\item \isa {bexE} (theorem), \bold{92}
\item \isa {bexI} (theorem), \bold{92}
\item \isa {bij_def} (theorem), \bold{94}
\item bijections, \hyperpage{94}
\item binomial coefficients, \hyperpage{93}
\item bisimulations, \hyperpage{100}
\item \isa {blast} (method), \hyperpage{72--75}
\item \isa {bool} (type), \hyperpage{2, 3}
\item \isa {bspec} (theorem), \bold{92}
\item \isacommand{by} (command), \hyperpage{57}
\indexspace
\item \isa {card} (constant), \hyperpage{93}
\item \isa {card_Pow} (theorem), \bold{93}
\item \isa {card_Un_Int} (theorem), \bold{93}
\item cardinality, \hyperpage{93}
\item \isa {case} (symbol), \bold{3}, \hyperpage{4}, \hyperpage{16},
\hyperpage{30, 31}
\item case distinction, \bold{17}
\item case splits, \bold{29}
\item \isa {case_tac} (method), \hyperpage{17}, \hyperpage{85}
\item \isa {clarify} (method), \hyperpage{74}, \hyperpage{76}
\item \isa {clarsimp} (method), \hyperpage{75, 76}
\item \isa {classical} (theorem), \bold{57}
\item coinduction, \bold{100}
\item \isa {Collect} (constant), \hyperpage{93}
\item \isa {comp_def} (theorem), \bold{96}
\item \isa {Compl_iff} (theorem), \bold{90}
\item complement
\subitem of a set, \hyperpage{89}
\item composition
\subitem of functions, \bold{94}
\subitem of relations, \bold{96}
\item congruence rules, \bold{157}
\item \isa {conjE} (theorem), \bold{55}
\item \isa {conjI} (theorem), \bold{52}
\item \isa {Cons} (constant), \hyperpage{7}
\item \isacommand {constdefs} (command), \hyperpage{23}
\item contrapositives, \hyperpage{57}
\item converse
\subitem of a relation, \bold{96}
\item \isa {converse_iff} (theorem), \bold{96}
\item CTL, \hyperpage{100--110}
\indexspace
\item \isacommand {datatype} (command), \hyperpage{7},
\hyperpage{36--42}
\item \isacommand {defer} (command), \hyperpage{14}, \hyperpage{84}
\item definitions, \bold{23}
\subitem unfolding, \bold{28}
\item \isacommand {defs} (command), \hyperpage{23}
\item descriptions
\subitem definite, \hyperpage{69}
\subitem indefinite, \hyperpage{70}
\item \isa {dest} (attribute), \hyperpage{86}
\item destruction rules, \hyperpage{55}
\item \isa {diff_mult_distrib} (theorem), \bold{133}
\item difference
\subitem of sets, \bold{90}
\item \isa {disjCI} (theorem), \bold{58}
\item \isa {disjE} (theorem), \bold{54}
\item \isa {div} (symbol), \hyperpage{20}
\item divides relation, \hyperpage{68}, \hyperpage{78},
\hyperpage{85--87}, \hyperpage{134}
\item division
\subitem by negative numbers, \hyperpage{135}
\subitem by zero, \hyperpage{134}
\subitem for type \protect\isa{nat}, \hyperpage{133}
\item domain
\subitem of a relation, \hyperpage{96}
\item \isa {Domain_iff} (theorem), \bold{96}
\item \isacommand {done} (command), \hyperpage{11}
\item \isa {drule_tac} (method), \hyperpage{60}, \hyperpage{80}
\item \isa {dvd_add} (theorem), \bold{134}
\item \isa {dvd_anti_sym} (theorem), \bold{134}
\item \isa {dvd_def} (theorem), \bold{134}
\indexspace
\item \isa {elim!} (attribute), \hyperpage{115}
\item elimination rules, \hyperpage{53--54}
\item \isa {Eps} (constant), \hyperpage{93}
\item equality
\subitem of functions, \bold{93}
\subitem of records, \hyperpage{143}
\subitem of sets, \bold{90}
\item \isa {equalityE} (theorem), \bold{90}
\item \isa {equalityI} (theorem), \bold{90}
\item \isa {erule} (method), \hyperpage{54}
\item \isa {erule_tac} (method), \hyperpage{60}
\item Euclid's algorithm, \hyperpage{85--87}
\item even numbers
\subitem defining inductively, \hyperpage{111--115}
\item \texttt {EX}, \bold{189}
\item \isa {Ex} (constant), \hyperpage{93}
\item \isa {exE} (theorem), \bold{66}
\item \isa {exI} (theorem), \bold{66}
\item \isa {ext} (theorem), \bold{93}
\item extensionality
\subitem for functions, \bold{93, 94}
\subitem for records, \hyperpage{143}
\subitem for sets, \bold{90}
\item \ttEXU, \bold{189}
\indexspace
\item \isa {False} (constant), \hyperpage{3}
\item \isa {fast} (method), \hyperpage{75, 76}
\item \isa {finite} (symbol), \hyperpage{93}
\item \isa {Finites} (constant), \hyperpage{93}
\item fixed points, \hyperpage{100}
\item flags, \hyperpage{3, 4}, \hyperpage{31}
\subitem setting and resetting, \hyperpage{3}
\item \isa {force} (method), \hyperpage{75, 76}
\item formulae, \bold{3}
\item forward proof, \hyperpage{76--82}
\item \isa {frule} (method), \hyperpage{67}
\item \isa {frule_tac} (method), \hyperpage{60}
\item \isa {fst} (constant), \hyperpage{21}
\item functions, \hyperpage{93--95}
\subitem total, \hyperpage{9}, \hyperpage{45--50}
\subitem underdefined, \hyperpage{165}
\indexspace
\item \isa {gcd} (constant), \hyperpage{76--78}, \hyperpage{85--87}
\item generalizing for induction, \hyperpage{113}
\item Girard, Jean-Yves, \fnote{55}
\item ground terms example, \hyperpage{119--124}
\indexspace
\item \isa {hd} (constant), \hyperpage{15}
\item higher-order pattern, \bold{159}
\item Hilbert's $\varepsilon$-operator, \hyperpage{69--71}
\item \isa {hypreal} (type), \hyperpage{137}
\indexspace
\item \isa {Id_def} (theorem), \bold{96}
\item \isa {id_def} (theorem), \bold{94}
\item identifier, \bold{4}
\subitem qualified, \bold{2}
\item identity function, \bold{94}
\item identity relation, \bold{96}
\item \isa {if} (symbol), \bold{3}, \hyperpage{4}
\item \isa {iff} (attribute), \hyperpage{73, 74}, \hyperpage{86},
\hyperpage{114}
\item \isa {iffD1} (theorem), \bold{78}
\item \isa {iffD2} (theorem), \bold{78}
\item image
\subitem under a function, \bold{95}
\subitem under a relation, \bold{96}
\item \isa {image_def} (theorem), \bold{95}
\item \isa {Image_iff} (theorem), \bold{96}
\item \isa {impI} (theorem), \bold{56}
\item implication, \hyperpage{56--57}
\item \isa {induct_tac} (method), \hyperpage{10}, \hyperpage{17},
\hyperpage{50}, \hyperpage{172}
\item induction, \hyperpage{168--175}
\subitem recursion, \hyperpage{49--50}
\subitem structural, \bold{17}
\subitem well-founded, \hyperpage{99}
\item \isacommand {inductive} (command), \hyperpage{111}
\item inductive definition
\subitem simultaneous, \hyperpage{125}
\item inductive definitions, \hyperpage{111--129}
\item \isacommand {inductive\_cases} (command), \hyperpage{115},
\hyperpage{123}
\item \isacommand{infixr} (annotation), \hyperpage{8}
\item \isa {inj_on_def} (theorem), \bold{94}
\item injections, \hyperpage{94}
\item inner syntax, \bold{9}
\item \isa {insert} (constant), \hyperpage{91}
\item \isa {insert} (method), \hyperpage{80--82}
\item instance, \bold{145}
\item \texttt {INT}, \bold{189}
\item \texttt {Int}, \bold{189}
\item \isa {int} (type), \hyperpage{135}
\item \isa {INT_iff} (theorem), \bold{92}
\item \isa {IntD1} (theorem), \bold{89}
\item \isa {IntD2} (theorem), \bold{89}
\item integers, \hyperpage{135}
\item \isa {INTER} (constant), \hyperpage{93}
\item \texttt {Inter}, \bold{189}
\item \isa {Inter_iff} (theorem), \bold{92}
\item intersection, \hyperpage{89}
\subitem indexed, \hyperpage{92}
\item \isa {IntI} (theorem), \bold{89}
\item \isa {intro} (method), \hyperpage{58}
\item \isa {intro!} (attribute), \hyperpage{112}
\item introduction rules, \hyperpage{52--53}
\item \isa {inv} (constant), \hyperpage{70}
\item \isa {inv_image_def} (theorem), \bold{99}
\item inverse
\subitem of a function, \bold{94}
\subitem of a relation, \bold{96}
\item inverse image
\subitem of a function, \hyperpage{95}
\subitem of a relation, \hyperpage{98}
\indexspace
\item \isacommand {kill} (command), \hyperpage{14}
\indexspace
\item \isa {LEAST} (symbol), \hyperpage{21}, \hyperpage{69}
\item least number operator, \see{\protect\isa{LEAST}}{69}
\item \isacommand {lemma} (command), \hyperpage{11}
\item \isacommand {lemmas} (command), \hyperpage{77}, \hyperpage{86}
\item \isa {length} (symbol), \hyperpage{15}
\item \isa {length_induct}, \bold{172}
\item \isa {less_than} (constant), \hyperpage{98}
\item \isa {less_than_iff} (theorem), \bold{98}
\item \isa {let} (symbol), \bold{3}, \hyperpage{4}, \hyperpage{29}
\item \isa {lex_prod_def} (theorem), \bold{99}
\item lexicographic product, \bold{99}, \hyperpage{160}
\item {\texttt{lfp}}
\subitem applications of, \see{CTL}{100}
\item linear arithmetic, \hyperpage{20--21}, \hyperpage{31},
\hyperpage{131}
\item \isa {List} (theory), \hyperpage{15}
\item \isa {list} (type), \hyperpage{2}, \hyperpage{7},
\hyperpage{15}
\item \isa {lists_mono} (theorem), \bold{121}
\item Lowe, Gavin, \hyperpage{178--179}
\indexspace
\item \isa {Main} (theory), \hyperpage{2}
\item major premise, \bold{59}
\item \isa {max} (constant), \hyperpage{20, 21}
\item measure function, \bold{45}, \bold{98}
\item \isa {measure_def} (theorem), \bold{99}
\item meta-logic, \bold{64}
\item methods, \bold{14}
\item \isa {min} (constant), \hyperpage{20, 21}
\item \isa {mod} (symbol), \hyperpage{20}
\item \isa {mod_div_equality} (theorem), \bold{133}
\item \isa {mod_mult_distrib} (theorem), \bold{133}
\item \emph{modus ponens}, \hyperpage{51}, \hyperpage{56}
\item \isa {mono_def} (theorem), \bold{100}
\item monotone functions, \bold{100}, \hyperpage{123}
\subitem and inductive definitions, \hyperpage{121--122}
\item \isa {more} (constant), \hyperpage{140--142}
\item \isa {mp} (theorem), \bold{56}
\item multiset ordering, \bold{99}
\indexspace
\item \isa {nat} (type), \hyperpage{2}, \hyperpage{20},
\hyperpage{133--134}
\item natural deduction, \hyperpage{51--52}
\item natural numbers, \hyperpage{133--134}
\item Needham-Schroeder protocol, \hyperpage{177--179}
\item negation, \hyperpage{57--59}
\item \isa {Nil} (constant), \hyperpage{7}
\item \isa {no_asm}, \bold{27}
\item \isa {no_asm_simp}, \bold{27}
\item \isa {no_asm_use}, \bold{28}
\item non-standard reals, \hyperpage{137}
\item \isa {None} (constant), \bold{22}
\item \isa {notE} (theorem), \bold{57}
\item \isa {notI} (theorem), \bold{57}
\item numeric literals, \hyperpage{132}
\subitem for type \protect\isa{nat}, \hyperpage{133}
\subitem for type \protect\isa{real}, \hyperpage{136}
\indexspace
\item \isa {O} (symbol), \hyperpage{96}
\item \texttt {o}, \bold{189}
\item \isa {o_def} (theorem), \bold{94}
\item \isa {OF} (attribute), \hyperpage{78--79}
\item \isa {of} (attribute), \hyperpage{77}, \hyperpage{79}
\item \isacommand {oops} (command), \hyperpage{11}
\item \isa {option} (type), \bold{22}
\item ordered rewriting, \bold{158}
\item outer syntax, \bold{9}
\item overloading, \hyperpage{144--146}
\subitem and arithmetic, \hyperpage{132}
\indexspace
\item pairs and tuples, \hyperpage{21}, \hyperpage{137--140}
\item parent theory, \bold{2}
\item partial function, \hyperpage{164}
\item pattern, higher-order, \bold{159}
\item PDL, \hyperpage{102--105}
\item permutative rewrite rule, \bold{158}
\item \isacommand {pr} (command), \hyperpage{14}, \hyperpage{83}
\item \isacommand {prefer} (command), \hyperpage{14}, \hyperpage{84}
\item primitive recursion, \see{\isacommand{primrec}}{1}
\item \isacommand {primrec} (command), \hyperpage{8}, \hyperpage{16},
\hyperpage{36--42}
\item product type, \see{pairs and tuples}{1}
\item Proof General, \bold{5}
\item proofs
\subitem abandoning, \bold{11}
\subitem examples of failing, \hyperpage{71--72}
\item protocols
\subitem security, \hyperpage{177--187}
\indexspace
\item quantifiers
\subitem and inductive definitions, \hyperpage{119--121}
\subitem existential, \hyperpage{66}
\subitem for sets, \hyperpage{92}
\subitem instantiating, \hyperpage{68}
\subitem universal, \hyperpage{63--66}
\indexspace
\item \isa {r_into_rtrancl} (theorem), \bold{96}
\item \isa {r_into_trancl} (theorem), \bold{97}
\item range
\subitem of a function, \hyperpage{95}
\subitem of a relation, \hyperpage{96}
\item \isa {range} (symbol), \hyperpage{95}
\item \isa {Range_iff} (theorem), \bold{96}
\item \isa {Real} (theory), \hyperpage{137}
\item \isa {real} (type), \hyperpage{136--137}
\item real numbers, \hyperpage{136--137}
\item \isacommand {recdef} (command), \hyperpage{45--50},
\hyperpage{98}, \hyperpage{160--168}
\subitem and numeric literals, \hyperpage{132}
\item \isa {recdef_cong} (attribute), \hyperpage{164}
\item \isa {recdef_simp} (attribute), \hyperpage{47}
\item \isa {recdef_wf} (attribute), \hyperpage{162}
\item \isacommand {record} (command), \hyperpage{140}
\item \isa {record_split} (method), \hyperpage{143}
\item records, \hyperpage{140--144}
\subitem extensible, \hyperpage{141--142}
\item recursion
\subitem well-founded, \bold{161}
\item recursion induction, \hyperpage{49--50}
\item \isacommand {redo} (command), \hyperpage{14}
\item reflexive and transitive closure, \hyperpage{96--98}
\item relations, \hyperpage{95--98}
\subitem well-founded, \hyperpage{98--99}
\item \isa {rename_tac} (method), \hyperpage{66--67}
\item \isa {rev} (constant), \hyperpage{8}
\item rewrite rule, \bold{26}
\subitem permutative, \bold{158}
\item rewriting, \bold{26}
\subitem ordered, \bold{158}
\item \isa {rotate_tac} (method), \hyperpage{28}
\item \isa {rtrancl_refl} (theorem), \bold{96}
\item \isa {rtrancl_trans} (theorem), \bold{96}
\item rule induction, \hyperpage{112--114}
\item rule inversion, \hyperpage{114--115}, \hyperpage{123--124}
\item \isa {rule_tac} (method), \hyperpage{60}
\subitem and renaming, \hyperpage{67}
\indexspace
\item \isa {safe} (method), \hyperpage{75, 76}
\item safe rules, \bold{73}
\item \isa {set} (type), \hyperpage{2}, \hyperpage{89}
\item set comprehensions, \hyperpage{91--92}
\item \isa {set_ext} (theorem), \bold{90}
\item sets, \hyperpage{89--93}
\subitem finite, \hyperpage{93}
\subitem notation for finite, \bold{91}
\item settings, \see{flags}{1}
\item \isa {show_brackets} (flag), \hyperpage{4}
\item \isa {show_types} (flag), \hyperpage{3}
\item \texttt {show_types}, \hyperpage{14}
\item \isa {simp} (attribute), \bold{9}, \hyperpage{26}
\item \isa {simp} (method), \bold{26}
\item \isa {simp_all} (method), \hyperpage{26}, \hyperpage{36}
\item simplification, \hyperpage{25--32}, \hyperpage{157--160}
\subitem of let-expressions, \hyperpage{29}
\subitem ordered, \bold{158}
\subitem with definitions, \hyperpage{28}
\subitem with/of assumptions, \hyperpage{27}
\item simplification rule, \bold{26}, \hyperpage{159--160}
\item \isa {simplified} (attribute), \hyperpage{77}, \hyperpage{79}
\item simplifier, \bold{25}
\item \isa {size} (constant), \hyperpage{15}
\item \isa {snd} (constant), \hyperpage{21}
\item \isa {SOME} (symbol), \hyperpage{69}
\item \texttt {SOME}, \bold{189}
\item \isa {Some} (constant), \bold{22}
\item \isa {some_equality} (theorem), \bold{69}
\item \isa {someI} (theorem), \bold{70}
\item \isa {someI2} (theorem), \bold{70}
\item \isa {someI_ex} (theorem), \bold{71}
\item sorts, \hyperpage{150}
\item \isa {spec} (theorem), \bold{64}
\item \isa {split} (constant), \bold{137}
\item \isa {split} (method, attr.), \hyperpage{29--31}
\item split rule, \bold{30}
\item \isa {split_if} (theorem), \hyperpage{30}
\item \isa {ssubst} (theorem), \bold{61}
\item structural induction, \bold{17}
\item \isa {subgoal_tac} (method), \hyperpage{81, 82}
\item subset relation, \bold{90}
\item \isa {subsetD} (theorem), \bold{90}
\item \isa {subsetI} (theorem), \bold{90}
\item \isa {subst} (method), \hyperpage{61}
\item substitution, \hyperpage{61--63}
\item \isa {Suc} (constant), \hyperpage{20}
\item \isa {surj_def} (theorem), \bold{94}
\item surjections, \hyperpage{94}
\item \isa {sym} (theorem), \bold{77}
\item syntax translations, \hyperpage{23--24}
\indexspace
\item tacticals, \hyperpage{82--83}
\item tactics, \hyperpage{10}
\item \isacommand {term} (command), \hyperpage{14}
\item term rewriting, \bold{26}
\item termination, \see{functions, total}{1}
\item terms, \hyperpage{3}
\item \isa {THEN} (attribute), \bold{77}, \hyperpage{79},
\hyperpage{86}
\item \isacommand {theorem} (command), \bold{9}, \hyperpage{11}
\item theories, \hyperpage{2}
\subitem abandoning, \bold{14}
\item theory files, \hyperpage{2}
\item \isacommand {thm} (command), \hyperpage{14}
\item \isa {tl} (constant), \hyperpage{15}
\item \isa {trace_simp} (flag), \hyperpage{31}
\item tracing the simplifier, \bold{31}
\item \isa {trancl_trans} (theorem), \bold{97}
\item \isa {True} (constant), \hyperpage{3}
\item tuples, \see{pairs and tuples}{1}
\item \isacommand {typ} (command), \hyperpage{14}
\item type constraints, \bold{4}
\item type inference, \bold{3}
\item type synonyms, \hyperpage{22--23}
\item type variables, \bold{3}
\item \isacommand {typedecl} (command), \hyperpage{150}
\item \isacommand {typedef} (command), \hyperpage{151--155}
\item types, \hyperpage{2}
\subitem declaring, \hyperpage{150--151}
\subitem defining, \hyperpage{151--155}
\item \isacommand {types} (command), \hyperpage{22}
\indexspace
\item \texttt {UN}, \bold{189}
\item \texttt {Un}, \bold{189}
\item \isa {UN_E} (theorem), \bold{92}
\item \isa {UN_I} (theorem), \bold{92}
\item \isa {UN_iff} (theorem), \bold{92}
\item \isa {Un_subset_iff} (theorem), \bold{90}
\item \isacommand {undo} (command), \hyperpage{14}
\item unification, \hyperpage{60--63}
\item \isa {UNION} (constant), \hyperpage{93}
\item \texttt {Union}, \bold{189}
\item union
\subitem indexed, \hyperpage{92}
\item \isa {Union_iff} (theorem), \bold{92}
\item \isa {unit} (type), \hyperpage{22}
\item unknowns, \hyperpage{4}, \bold{52}
\item unsafe rules, \bold{73}
\item updating a function, \bold{93}
\indexspace
\item variable, \bold{4}
\item variables
\subitem schematic, \hyperpage{4}
\subitem type, \bold{3}
\item \isa {vimage_def} (theorem), \bold{95}
\indexspace
\item \isa {wf_induct} (theorem), \bold{99}
\item \isa {while} (constant), \hyperpage{167}
\item \isa {While_Combinator} (theory), \hyperpage{167}
\end{theindex}