doc-src/TutorialI/tutorial.ind

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\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{?}, 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 \mathrel {\smash -}\mathrel {\mkern -3mu}\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 $}, \bold{20, 21}, \bold{189}
  \item \texttt {<=}, \bold{189}
  \item \texttt {<}, \bold{20, 21}
  \item \texttt{[]}, \bold{7}
  \item \texttt{\#}, \bold{7}
  \item \texttt{\at}, \bold{8}, 189
  \item \emph {$\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 \mathrel =\mathrel {\mkern -3mu}\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), 83
  \item \isa {<*lex*>}, \see{lexicographic product}{1}
  \item \isa {?} (tactical), 83
  \item \texttt{|} (tactical), 83

  \indexspace

  \item \isa {0} (constant), 20, 21, 133
  \item \isa {1} (symbol), 133
  \item \isa {2} (symbol), 133

  \indexspace

  \item abandoning a proof, \bold{11}
  \item abandoning a theory, \bold{14}
  \item \isa {abs} (constant), 135
  \item \texttt {abs}, \bold{189}
  \item absolute value, 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), 93
  \item \isa {allE} (theorem), \bold{65}
  \item \isa {allI} (theorem), \bold{64}
  \item \isacommand {apply} (command), 13
  \item \isa {arg_cong} (theorem), \bold{80}
  \item \isa {arith} (method), 21, 131
  \item \textsc {ascii} symbols, \bold{189}
  \item associative-commutative function, 158
  \item \isa {assumption} (method), 53
  \item assumptions
    \subitem renaming, 66--67
    \subitem reusing, 67
  \item \isa {auto} (method), 36, 76
  \item \isa {axclass}, 144--150
  \item axiom of choice, 70
  \item axiomatic type classes, 144--150

  \indexspace

  \item \isacommand {back} (command), 62
  \item \isa {Ball} (constant), 93
  \item \isa {ballI} (theorem), \bold{92}
  \item \isa {best} (method), 75, 76
  \item \isa {Bex} (constant), 93
  \item \isa {bexE} (theorem), \bold{92}
  \item \isa {bexI} (theorem), \bold{92}
  \item \isa {bij_def} (theorem), \bold{94}
  \item bijections, 94
  \item binomial coefficients, 93
  \item bisimulations, 100
  \item \isa {blast} (method), 72--75
  \item \isa {bool} (type), 2, 3
  \item \isa {bspec} (theorem), \bold{92}
  \item \isacommand{by} (command), 57

  \indexspace

  \item \isa {card} (constant), 93
  \item \isa {card_Pow} (theorem), \bold{93}
  \item \isa {card_Un_Int} (theorem), \bold{93}
  \item cardinality, 93
  \item \isa {case} (symbol), \bold{3}, 4, 16, 30, 31
  \item case distinction, \bold{17}
  \item case splits, \bold{29}
  \item \isa {case_tac} (method), 17, 85
  \item \isa {clarify} (method), 74, 76
  \item \isa {clarsimp} (method), 75, 76
  \item \isa {classical} (theorem), \bold{57}
  \item coinduction, \bold{100}
  \item \isa {Collect} (constant), 93
  \item \isa {comp_def} (theorem), \bold{96}
  \item \isa {Compl_iff} (theorem), \bold{90}
  \item complement
    \subitem of a set, 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), 7
  \item \isacommand {constdefs} (command), 23
  \item contrapositives, 57
  \item converse
    \subitem of a relation, \bold{96}
  \item \isa {converse_iff} (theorem), \bold{96}
  \item CTL, 100--110

  \indexspace

  \item \isacommand {datatype} (command), 7, 36--42
  \item \isacommand {defer} (command), 14, 84
  \item definitions, \bold{23}
    \subitem unfolding, \bold{28}
  \item \isacommand {defs} (command), 23
  \item descriptions
    \subitem definite, 69
    \subitem indefinite, 70
  \item \isa {dest} (attribute), 86
  \item destruction rules, 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), 20
  \item divides relation, 68, 78, 85--87, 134
  \item division
    \subitem by negative numbers, 135
    \subitem by zero, 134
    \subitem for type \protect\isa{nat}, 133
  \item domain
    \subitem of a relation, 96
  \item \isa {Domain_iff} (theorem), \bold{96}
  \item \isacommand {done} (command), 11
  \item \isa {drule_tac} (method), 60, 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), 115
  \item elimination rules, 53--54
  \item \isa {Eps} (constant), 93
  \item equality
    \subitem of functions, \bold{93}
    \subitem of records, 143
    \subitem of sets, \bold{90}
  \item \isa {equalityE} (theorem), \bold{90}
  \item \isa {equalityI} (theorem), \bold{90}
  \item \isa {erule} (method), 54
  \item \isa {erule_tac} (method), 60
  \item Euclid's algorithm, 85--87
  \item even numbers
    \subitem defining inductively, 111--115
  \item \texttt {EX}, \bold{189}
  \item \isa {Ex} (constant), 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, 143
    \subitem for sets, \bold{90}
  \item \ttEXU, \bold{189}

  \indexspace

  \item \isa {False} (constant), 3
  \item \isa {fast} (method), 75, 76
  \item \isa {finite} (symbol), 93
  \item \isa {Finites} (constant), 93
  \item fixed points, 100
  \item flags, 3, 4, 31
    \subitem setting and resetting, 3
  \item \isa {force} (method), 75, 76
  \item formulae, \bold{3}
  \item forward proof, 76--82
  \item \isa {frule} (method), 67
  \item \isa {frule_tac} (method), 60
  \item \isa {fst} (constant), 21
  \item functions, 93--95
    \subitem total, 9, 45--50
    \subitem underdefined, 165

  \indexspace

  \item \isa {gcd} (constant), 76--78, 85--87
  \item generalizing for induction, 113
  \item Girard, Jean-Yves, \fnote{55}
  \item ground terms example, 119--124

  \indexspace

  \item \isa {hd} (constant), 15
  \item higher-order pattern, \bold{159}
  \item Hilbert's $\varepsilon$-operator, 69--71
  \item \isa {hypreal} (type), 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}, 4
  \item \isa {iff} (attribute), 73, 74, 86, 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, 56--57
  \item \isa {induct_tac} (method), 10, 17, 50, 172
  \item induction, 168--175
    \subitem recursion, 49--50
    \subitem structural, \bold{17}
    \subitem well-founded, 99
  \item \isacommand {inductive} (command), 111
  \item inductive definition
    \subitem simultaneous, 125
  \item inductive definitions, 111--129
  \item \isacommand {inductive\_cases} (command), 115, 123
  \item \isacommand{infixr} (annotation), 8
  \item \isa {inj_on_def} (theorem), \bold{94}
  \item injections, 94
  \item inner syntax, \bold{9}
  \item \isa {insert} (constant), 91
  \item \isa {insert} (method), 80--82
  \item instance, \bold{145}
  \item \texttt {INT}, \bold{189}
  \item \texttt {Int}, \bold{189}
  \item \isa {int} (type), 135
  \item \isa {INT_iff} (theorem), \bold{92}
  \item \isa {IntD1} (theorem), \bold{89}
  \item \isa {IntD2} (theorem), \bold{89}
  \item integers, 135
  \item \isa {INTER} (constant), 93
  \item \texttt {Inter}, \bold{189}
  \item \isa {Inter_iff} (theorem), \bold{92}
  \item intersection, 89
    \subitem indexed, 92
  \item \isa {IntI} (theorem), \bold{89}
  \item \isa {intro} (method), 58
  \item \isa {intro!} (attribute), 112
  \item introduction rules, 52--53
  \item \isa {inv} (constant), 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, 95
    \subitem of a relation, 98

  \indexspace

  \item \isacommand {kill} (command), 14

  \indexspace

  \item \isa {LEAST} (symbol), 21, 69
  \item least number operator, \see{\protect\isa{LEAST}}{69}
  \item \isacommand {lemma} (command), 11
  \item \isacommand {lemmas} (command), 77, 86
  \item \isa {length} (symbol), 15
  \item \isa {length_induct}, \bold{172}
  \item \isa {less_than} (constant), 98
  \item \isa {less_than_iff} (theorem), \bold{98}
  \item \isa {let} (symbol), \bold{3}, 4, 29
  \item \isa {lex_prod_def} (theorem), \bold{99}
  \item lexicographic product, \bold{99}, 160
  \item {\texttt{lfp}}
    \subitem applications of, \see{CTL}{100}
  \item linear arithmetic, 20--21, 31, 131
  \item \isa {List} (theory), 15
  \item \isa {list} (type), 2, 7, 15
  \item \isa {lists_mono} (theorem), \bold{121}
  \item Lowe, Gavin, 178--179

  \indexspace

  \item \isa {Main} (theory), 2
  \item major premise, \bold{59}
  \item \isa {max} (constant), 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), 20, 21
  \item \isa {mod} (symbol), 20
  \item \isa {mod_div_equality} (theorem), \bold{133}
  \item \isa {mod_mult_distrib} (theorem), \bold{133}
  \item \emph{modus ponens}, 51, 56
  \item \isa {mono_def} (theorem), \bold{100}
  \item monotone functions, \bold{100}, 123
    \subitem and inductive definitions, 121--122
  \item \isa {more} (constant), 140--142
  \item \isa {mp} (theorem), \bold{56}
  \item multiset ordering, \bold{99}

  \indexspace

  \item \isa {nat} (type), 2, 20, 133--134
  \item natural deduction, 51--52
  \item natural numbers, 133--134
  \item Needham-Schroeder protocol, 177--179
  \item negation, 57--59
  \item \isa {Nil} (constant), 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, 137
  \item \isa {None} (constant), \bold{22}
  \item \isa {notE} (theorem), \bold{57}
  \item \isa {notI} (theorem), \bold{57}
  \item numeric literals, 132
    \subitem for type \protect\isa{nat}, 133
    \subitem for type \protect\isa{real}, 136

  \indexspace

  \item \isa {O} (symbol), 96
  \item \texttt {o}, \bold{189}
  \item \isa {o_def} (theorem), \bold{94}
  \item \isa {OF} (attribute), 78--79
  \item \isa {of} (attribute), 77, 79
  \item \isacommand {oops} (command), 11
  \item \isa {option} (type), \bold{22}
  \item ordered rewriting, \bold{158}
  \item outer syntax, \bold{9}
  \item overloading, 144--146
    \subitem and arithmetic, 132

  \indexspace

  \item pairs and tuples, 21, 137--140
  \item parent theory, \bold{2}
  \item partial function, 164
  \item pattern, higher-order, \bold{159}
  \item PDL, 102--105
  \item permutative rewrite rule, \bold{158}
  \item \isacommand {pr} (command), 14, 83
  \item \isacommand {prefer} (command), 14, 84
  \item primitive recursion, \see{\isacommand{primrec}}{1}
  \item \isacommand {primrec} (command), 8, 16, 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, 71--72
  \item protocols
    \subitem security, 177--187

  \indexspace

  \item quantifiers
    \subitem and inductive definitions, 119--121
    \subitem existential, 66
    \subitem for sets, 92
    \subitem instantiating, 68
    \subitem universal, 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, 95
    \subitem of a relation, 96
  \item \isa {range} (symbol), 95
  \item \isa {Range_iff} (theorem), \bold{96}
  \item \isa {Real} (theory), 137
  \item \isa {real} (type), 136--137
  \item real numbers, 136--137
  \item \isacommand {recdef} (command), 45--50, 98, 160--168
    \subitem and numeric literals, 132
  \item \isa {recdef_cong} (attribute), 164
  \item \isa {recdef_simp} (attribute), 47
  \item \isa {recdef_wf} (attribute), 162
  \item \isacommand {record} (command), 140
  \item \isa {record_split} (method), 143
  \item records, 140--144
    \subitem extensible, 141--142
  \item recursion
    \subitem well-founded, \bold{161}
  \item recursion induction, 49--50
  \item \isacommand {redo} (command), 14
  \item reflexive and transitive closure, 96--98
  \item relations, 95--98
    \subitem well-founded, 98--99
  \item \isa {rename_tac} (method), 66--67
  \item \isa {rev} (constant), 8
  \item rewrite rule, \bold{26}
    \subitem permutative, \bold{158}
  \item rewriting, \bold{26}
    \subitem ordered, \bold{158}
  \item \isa {rotate_tac} (method), 28
  \item \isa {rtrancl_refl} (theorem), \bold{96}
  \item \isa {rtrancl_trans} (theorem), \bold{96}
  \item rule induction, 112--114
  \item rule inversion, 114--115, 123--124
  \item \isa {rule_tac} (method), 60
    \subitem and renaming, 67

  \indexspace

  \item \isa {safe} (method), 75, 76
  \item safe rules, \bold{73}
  \item \isa {set} (type), 2, 89
  \item set comprehensions, 91--92
  \item \isa {set_ext} (theorem), \bold{90}
  \item sets, 89--93
    \subitem finite, 93
    \subitem notation for finite, \bold{91}
  \item settings, \see{flags}{1}
  \item \isa {show_brackets} (flag), 4
  \item \isa {show_types} (flag), 3
  \item \texttt {show_types}, 14
  \item \isa {simp} (attribute), \bold{9}, 26
  \item \isa {simp} (method), \bold{26}
  \item \isa {simp_all} (method), 26, 36
  \item simplification, 25--32, 157--160
    \subitem of let-expressions, 29
    \subitem ordered, \bold{158}
    \subitem with definitions, 28
    \subitem with/of assumptions, 27
  \item simplification rule, \bold{26}, 159--160
  \item \isa {simplified} (attribute), 77, 79
  \item simplifier, \bold{25}
  \item \isa {size} (constant), 15
  \item \isa {snd} (constant), 21
  \item \isa {SOME} (symbol), 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, 150
  \item \isa {spec} (theorem), \bold{64}
  \item \isa {split} (constant), \bold{137}
  \item \isa {split} (method, attr.), 29--31
  \item split rule, \bold{30}
  \item \isa {split_if} (theorem), 30
  \item \isa {ssubst} (theorem), \bold{61}
  \item structural induction, \bold{17}
  \item \isa {subgoal_tac} (method), 81, 82
  \item subset relation, \bold{90}
  \item \isa {subsetD} (theorem), \bold{90}
  \item \isa {subsetI} (theorem), \bold{90}
  \item \isa {subst} (method), 61
  \item substitution, 61--63
  \item \isa {Suc} (constant), 20
  \item \isa {surj_def} (theorem), \bold{94}
  \item surjections, 94
  \item \isa {sym} (theorem), \bold{77}

  \indexspace

  \item tacticals, 82--83
  \item tactics, 10
  \item \isacommand {term} (command), 14
  \item term rewriting, \bold{26}
  \item termination, \see{functions, total}{1}
  \item terms, 3
  \item \isa {THEN} (attribute), \bold{77}, 79, 86
  \item \isacommand {theorem} (command), \bold{9}, 11
  \item theories, 2
    \subitem abandoning, \bold{14}
  \item theory files, 2
  \item \isacommand {thm} (command), 14
  \item \isa {tl} (constant), 15
  \item \isa {trace_simp} (flag), 31
  \item tracing the simplifier, \bold{31}
  \item \isa {trancl_trans} (theorem), \bold{97}
  \item \isa {True} (constant), 3
  \item tuples, \see{pairs and tuples}{1}
  \item \isacommand {typ} (command), 14
  \item type constraints, \bold{4}
  \item type inference, \bold{3}
  \item type variables, \bold{3}
  \item \isacommand {typedecl} (command), 150
  \item \isacommand {typedef} (command), 151--155
  \item types, 2
    \subitem declaring, 150--151
    \subitem defining, 151--155
  \item \isacommand {types} (command), 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), 14
  \item unification, 60--63
  \item \isa {UNION} (constant), 93
  \item \texttt {Union}, \bold{189}
  \item union
    \subitem indexed, 92
  \item \isa {Union_iff} (theorem), \bold{92}
  \item \isa {unit} (type), 22
  \item unknowns, 4, \bold{52}
  \item unsafe rules, \bold{73}
  \item updating a function, \bold{93}

  \indexspace

  \item variable, \bold{4}
  \item variables
    \subitem schematic, 4
    \subitem type, \bold{3}
  \item \isa {vimage_def} (theorem), \bold{95}

  \indexspace

  \item \isa {wf_induct} (theorem), \bold{99}
  \item \isa {while} (constant), 167
  \item \isa {While_Combinator} (theory), 167

\end{theindex}