doc-src/TutorialI/tutorial.ind
changeset 13894 8018173a7979
parent 13893 19849d258890
child 13895 b6105462ccd3
equal deleted inserted replaced
13893:19849d258890 13894:8018173a7979
     1 \begin{theindex}
       
     2 
       
     3   \item \ttall, \bold{209}
       
     4   \item \texttt{?}, \bold{209}
       
     5   \item \isasymuniqex, \bold{209}
       
     6   \item \ttuniquex, \bold{209}
       
     7   \item {\texttt {\&}}, \bold{209}
       
     8   \item \verb$~$, \bold{209}
       
     9   \item \verb$~=$, \bold{209}
       
    10   \item \ttor, \bold{209}
       
    11   \item \texttt{[]}, \bold{9}
       
    12   \item \texttt{\#}, \bold{9}
       
    13   \item \texttt{\at}, \bold{10}, 209
       
    14   \item \isasymnotin, \bold{209}
       
    15   \item \verb$~:$, \bold{209}
       
    16   \item \isasymInter, \bold{209}
       
    17   \item \isasymUnion, \bold{209}
       
    18   \item \isasyminverse, \bold{209}
       
    19   \item \verb$^-1$, \bold{209}
       
    20   \item \isactrlsup{\isacharasterisk}, \bold{209}
       
    21   \item \verb$^$\texttt{*}, \bold{209}
       
    22   \item \isasymAnd, \bold{12}, \bold{209}
       
    23   \item \ttAnd, \bold{209}
       
    24   \item \emph {$\Rightarrow $}, \bold{5}
       
    25   \item \ttlbr, \bold{209}
       
    26   \item \ttrbr, \bold{209}
       
    27   \item \texttt {\%}, \bold{209}
       
    28   \item \texttt {;}, \bold{7}
       
    29   \item \isa {()} (constant), 24
       
    30   \item * trace_unify_fail (flag), 76
       
    31   \item \isa {+} (tactical), 99
       
    32   \item \isa {<*lex*>}, \see{lexicographic product}{1}
       
    33   \item \isa {?} (tactical), 100
       
    34   \item \texttt{|} (tactical), 100
       
    35 
       
    36   \indexspace
       
    37 
       
    38   \item \isa {0} (constant), 22, 23, 150
       
    39   \item \isa {1} (constant), 23, 150, 151
       
    40 
       
    41   \indexspace
       
    42 
       
    43   \item abandoning a proof, \bold{13}
       
    44   \item abandoning a theory, \bold{16}
       
    45   \item \isa {abs} (constant), 153
       
    46   \item \texttt {abs}, \bold{209}
       
    47   \item absolute value, 153
       
    48   \item \isa {add} (modifier), 29
       
    49   \item \isa {add_ac} (theorems), 152
       
    50   \item \isa {add_assoc} (theorem), \bold{152}
       
    51   \item \isa {add_commute} (theorem), \bold{152}
       
    52   \item \isa {add_mult_distrib} (theorem), \bold{151}
       
    53   \item \texttt {ALL}, \bold{209}
       
    54   \item \isa {All} (constant), 109
       
    55   \item \isa {allE} (theorem), \bold{81}
       
    56   \item \isa {allI} (theorem), \bold{80}
       
    57   \item antiquotation, \bold{61}
       
    58   \item append function, 10--14
       
    59   \item \isacommand {apply} (command), 15
       
    60   \item \isa {arg_cong} (theorem), \bold{96}
       
    61   \item \isa {arith} (method), 23, 149
       
    62   \item arithmetic operations
       
    63     \subitem for \protect\isa{nat}, 23
       
    64   \item \textsc {ascii} symbols, \bold{209}
       
    65   \item Aspinall, David, viii
       
    66   \item associative-commutative function, 176
       
    67   \item \isa {assumption} (method), 69
       
    68   \item assumptions
       
    69     \subitem of subgoal, 12
       
    70     \subitem renaming, 83
       
    71     \subitem reusing, 83--84
       
    72   \item \isa {auto} (method), 38, 92
       
    73   \item \isa {axclass}, 164--171
       
    74   \item axiom of choice, 87
       
    75   \item axiomatic type classes, 164--171
       
    76 
       
    77   \indexspace
       
    78 
       
    79   \item \isacommand {back} (command), 79
       
    80   \item \isa {Ball} (constant), 109
       
    81   \item \isa {ballI} (theorem), \bold{108}
       
    82   \item \isa {best} (method), 92
       
    83   \item \isa {Bex} (constant), 109
       
    84   \item \isa {bexE} (theorem), \bold{108}
       
    85   \item \isa {bexI} (theorem), \bold{108}
       
    86   \item \isa {bij_def} (theorem), \bold{110}
       
    87   \item bijections, 110
       
    88   \item binary trees, 18
       
    89   \item binomial coefficients, 109
       
    90   \item bisimulations, 116
       
    91   \item \isa {blast} (method), 89--92
       
    92   \item \isa {bool} (type), 4, 5
       
    93   \item boolean expressions example, 20--22
       
    94   \item \isa {bspec} (theorem), \bold{108}
       
    95   \item \isacommand{by} (command), 73
       
    96 
       
    97   \indexspace
       
    98 
       
    99   \item \isa {card} (constant), 109
       
   100   \item \isa {card_Pow} (theorem), \bold{109}
       
   101   \item \isa {card_Un_Int} (theorem), \bold{109}
       
   102   \item cardinality, 109
       
   103   \item \isa {case} (symbol), 32, 33
       
   104   \item \isa {case} expressions, 5, 6, 18
       
   105   \item case distinctions, 19
       
   106   \item case splits, \bold{31}
       
   107   \item \isa {case_tac} (method), 19, 102, 158
       
   108   \item \isa {cases} (method), 162
       
   109   \item \isacommand {chapter} (command), 59
       
   110   \item \isa {clarify} (method), 91, 92
       
   111   \item \isa {clarsimp} (method), 91, 92
       
   112   \item \isa {classical} (theorem), \bold{73}
       
   113   \item coinduction, \bold{116}
       
   114   \item \isa {Collect} (constant), 109
       
   115   \item compiling expressions example, 36--38
       
   116   \item \isa {Compl_iff} (theorem), \bold{106}
       
   117   \item complement
       
   118     \subitem of a set, 105
       
   119   \item composition
       
   120     \subitem of functions, \bold{110}
       
   121     \subitem of relations, \bold{112}
       
   122   \item conclusion
       
   123     \subitem of subgoal, 12
       
   124   \item conditional expressions, \see{\isa{if} expressions}{1}
       
   125   \item conditional simplification rules, 31
       
   126   \item \isa {cong} (attribute), 176
       
   127   \item congruence rules, \bold{175}
       
   128   \item \isa {conjE} (theorem), \bold{71}
       
   129   \item \isa {conjI} (theorem), \bold{68}
       
   130   \item \isa {Cons} (constant), 9
       
   131   \item \isacommand {constdefs} (command), 25
       
   132   \item \isacommand {consts} (command), 10
       
   133   \item contrapositives, 73
       
   134   \item converse
       
   135     \subitem of a relation, \bold{112}
       
   136   \item \isa {converse_iff} (theorem), \bold{112}
       
   137   \item CTL, 121--126, 191--193
       
   138 
       
   139   \indexspace
       
   140 
       
   141   \item \isacommand {datatype} (command), 9, 38--44
       
   142   \item datatypes, 17--22
       
   143     \subitem and nested recursion, 40, 44
       
   144     \subitem mutually recursive, 38
       
   145     \subitem nested, 180
       
   146   \item \isacommand {defer} (command), 16, 101
       
   147   \item Definitional Approach, 26
       
   148   \item definitions, \bold{25}
       
   149     \subitem unfolding, \bold{30}
       
   150   \item \isacommand {defs} (command), 25
       
   151   \item \isa {del} (modifier), 29
       
   152   \item description operators, 85--87
       
   153   \item descriptions
       
   154     \subitem definite, 85
       
   155     \subitem indefinite, 86
       
   156   \item \isa {dest} (attribute), 103
       
   157   \item destruction rules, 71
       
   158   \item \isa {diff_mult_distrib} (theorem), \bold{151}
       
   159   \item difference
       
   160     \subitem of sets, \bold{106}
       
   161   \item \isa {disjCI} (theorem), \bold{74}
       
   162   \item \isa {disjE} (theorem), \bold{70}
       
   163   \item \isa {div} (symbol), 23
       
   164   \item divides relation, 84, 95, 102--104, 152
       
   165   \item division
       
   166     \subitem by negative numbers, 153
       
   167     \subitem by zero, 152
       
   168     \subitem for type \protect\isa{nat}, 151
       
   169   \item documents, \bold{57}
       
   170   \item domain
       
   171     \subitem of a relation, 112
       
   172   \item \isa {Domain_iff} (theorem), \bold{112}
       
   173   \item \isacommand {done} (command), 13
       
   174   \item \isa {drule_tac} (method), 76, 96
       
   175   \item \isa {dvd_add} (theorem), \bold{152}
       
   176   \item \isa {dvd_anti_sym} (theorem), \bold{152}
       
   177   \item \isa {dvd_def} (theorem), \bold{152}
       
   178 
       
   179   \indexspace
       
   180 
       
   181   \item \isa {elim!} (attribute), 131
       
   182   \item elimination rules, 69--70
       
   183   \item \isacommand {end} (command), 14
       
   184   \item \isa {Eps} (constant), 109
       
   185   \item equality, 6
       
   186     \subitem of functions, \bold{109}
       
   187     \subitem of records, 161
       
   188     \subitem of sets, \bold{106}
       
   189   \item \isa {equalityE} (theorem), \bold{106}
       
   190   \item \isa {equalityI} (theorem), \bold{106}
       
   191   \item \isa {erule} (method), 70
       
   192   \item \isa {erule_tac} (method), 76
       
   193   \item Euclid's algorithm, 102--104
       
   194   \item even numbers
       
   195     \subitem defining inductively, 127--131
       
   196   \item \texttt {EX}, \bold{209}
       
   197   \item \isa {Ex} (constant), 109
       
   198   \item \isa {exE} (theorem), \bold{82}
       
   199   \item \isa {exI} (theorem), \bold{82}
       
   200   \item \isa {ext} (theorem), \bold{109}
       
   201   \item \isa {extend} (constant), 163
       
   202   \item extensionality
       
   203     \subitem for functions, \bold{109, 110}
       
   204     \subitem for records, 162
       
   205     \subitem for sets, \bold{106}
       
   206   \item \ttEXU, \bold{209}
       
   207 
       
   208   \indexspace
       
   209 
       
   210   \item \isa {False} (constant), 5
       
   211   \item \isa {fast} (method), 92, 124
       
   212   \item Fibonacci function, 47
       
   213   \item \isa {fields} (constant), 163
       
   214   \item \isa {finite} (symbol), 109
       
   215   \item \isa {Finites} (constant), 109
       
   216   \item fixed points, 116
       
   217   \item flags, 5, 6, 33, 76
       
   218     \subitem setting and resetting, 5
       
   219   \item \isa {force} (method), 91, 92
       
   220   \item formal comments, \bold{61}
       
   221   \item formal proof documents, \bold{57}
       
   222   \item formulae, 5--6
       
   223   \item forward proof, 93--99
       
   224   \item \isa {frule} (method), 83--84
       
   225   \item \isa {frule_tac} (method), 76
       
   226   \item \isa {fst} (constant), 24
       
   227   \item function types, 5
       
   228   \item functions, 109--111
       
   229     \subitem partial, 182
       
   230     \subitem total, 11, 47--52
       
   231     \subitem underdefined, 183
       
   232 
       
   233   \indexspace
       
   234 
       
   235   \item \isa {gcd} (constant), 93--95, 102--104
       
   236   \item generalizing for induction, 129
       
   237   \item generalizing induction formulae, 34
       
   238   \item Girard, Jean-Yves, \fnote{71}
       
   239   \item Gordon, Mike, 3
       
   240   \item grammars
       
   241     \subitem defining inductively, 140--145
       
   242   \item ground terms example, 135--140
       
   243 
       
   244   \indexspace
       
   245 
       
   246   \item \isa {hd} (constant), 17, 37
       
   247   \item \isacommand {header} (command), 59
       
   248   \item Hilbert's $\varepsilon$-operator, 86
       
   249   \item \isacommand {hints} (command), 49, 180, 182
       
   250   \item HOLCF, 44
       
   251   \item Hopcroft, J. E., 145
       
   252   \item \isa {hypreal} (type), 155
       
   253 
       
   254   \indexspace
       
   255 
       
   256   \item \isa {Id_def} (theorem), \bold{112}
       
   257   \item \isa {id_def} (theorem), \bold{110}
       
   258   \item identifiers, \bold{6}
       
   259     \subitem qualified, \bold{4}
       
   260   \item identity function, \bold{110}
       
   261   \item identity relation, \bold{112}
       
   262   \item \isa {if} expressions, 5, 6
       
   263     \subitem simplification of, 33
       
   264     \subitem splitting of, 31, 49
       
   265   \item if-and-only-if, 6
       
   266   \item \isa {iff} (attribute), 90, 91, 103, 130
       
   267   \item \isa {iffD1} (theorem), \bold{94}
       
   268   \item \isa {iffD2} (theorem), \bold{94}
       
   269   \item ignored material, \bold{64}
       
   270   \item image
       
   271     \subitem under a function, \bold{111}
       
   272     \subitem under a relation, \bold{112}
       
   273   \item \isa {image_def} (theorem), \bold{111}
       
   274   \item \isa {Image_iff} (theorem), \bold{112}
       
   275   \item \isa {impI} (theorem), \bold{72}
       
   276   \item implication, 72--73
       
   277   \item \isa {ind_cases} (method), 131
       
   278   \item \isa {induct_tac} (method), 12, 19, 52, 190
       
   279   \item induction, 186--193
       
   280     \subitem complete, 188
       
   281     \subitem deriving new schemas, 190
       
   282     \subitem on a term, 187
       
   283     \subitem recursion, 51--52
       
   284     \subitem structural, 19
       
   285     \subitem well-founded, 115
       
   286   \item induction heuristics, 33--35
       
   287   \item \isacommand {inductive} (command), 127
       
   288   \item inductive definition
       
   289     \subitem simultaneous, 141
       
   290   \item inductive definitions, 127--145
       
   291   \item \isacommand {inductive\_cases} (command), 131, 139
       
   292   \item infinitely branching trees, 43
       
   293   \item infix annotations, 53
       
   294   \item \isacommand{infixr} (annotation), 10
       
   295   \item \isa {inj_on_def} (theorem), \bold{110}
       
   296   \item injections, 110
       
   297   \item \isa {insert} (constant), 107
       
   298   \item \isa {insert} (method), 97--99
       
   299   \item instance, \bold{166}
       
   300   \item \texttt {INT}, \bold{209}
       
   301   \item \texttt {Int}, \bold{209}
       
   302   \item \isa {int} (type), 153--154
       
   303   \item \isa {INT_iff} (theorem), \bold{108}
       
   304   \item \isa {IntD1} (theorem), \bold{105}
       
   305   \item \isa {IntD2} (theorem), \bold{105}
       
   306   \item integers, 153--154
       
   307   \item \isa {INTER} (constant), 109
       
   308   \item \texttt {Inter}, \bold{209}
       
   309   \item \isa {Inter_iff} (theorem), \bold{108}
       
   310   \item intersection, 105
       
   311     \subitem indexed, 108
       
   312   \item \isa {IntI} (theorem), \bold{105}
       
   313   \item \isa {intro} (method), 74
       
   314   \item \isa {intro!} (attribute), 128
       
   315   \item \isa {intro_classes} (method), 166
       
   316   \item introduction rules, 68--69
       
   317   \item \isa {inv} (constant), 86
       
   318   \item \isa {inv_image_def} (theorem), \bold{115}
       
   319   \item inverse
       
   320     \subitem of a function, \bold{110}
       
   321     \subitem of a relation, \bold{112}
       
   322   \item inverse image
       
   323     \subitem of a function, 111
       
   324     \subitem of a relation, 114
       
   325   \item \isa {itrev} (constant), 34
       
   326 
       
   327   \indexspace
       
   328 
       
   329   \item \isacommand {kill} (command), 16
       
   330 
       
   331   \indexspace
       
   332 
       
   333   \item $\lambda$ expressions, 5
       
   334   \item LCF, 43
       
   335   \item \isa {LEAST} (symbol), 23, 86
       
   336   \item least number operator, \see{\protect\isa{LEAST}}{86}
       
   337   \item Leibniz, Gottfried Wilhelm, 53
       
   338   \item \isacommand {lemma} (command), 13
       
   339   \item \isacommand {lemmas} (command), 93, 103
       
   340   \item \isa {length} (symbol), 18
       
   341   \item \isa {length_induct}, \bold{190}
       
   342   \item \isa {less_than} (constant), 114
       
   343   \item \isa {less_than_iff} (theorem), \bold{114}
       
   344   \item \isa {let} expressions, 5, 6, 31
       
   345   \item \isa {Let_def} (theorem), 31
       
   346   \item \isa {lex_prod_def} (theorem), \bold{115}
       
   347   \item lexicographic product, \bold{115}, 178
       
   348   \item {\texttt{lfp}}
       
   349     \subitem applications of, \see{CTL}{116}
       
   350   \item Library, 4
       
   351   \item linear arithmetic, 22--24, 149
       
   352   \item \isa {List} (theory), 17
       
   353   \item \isa {list} (type), 5, 9, 17
       
   354   \item \isa {list.split} (theorem), 32
       
   355   \item \isa {lists_mono} (theorem), \bold{137}
       
   356   \item Lowe, Gavin, 196--197
       
   357 
       
   358   \indexspace
       
   359 
       
   360   \item \isa {Main} (theory), 4
       
   361   \item major premise, \bold{75}
       
   362   \item \isa {make} (constant), 163
       
   363   \item marginal comments, \bold{61}
       
   364   \item markup commands, \bold{59}
       
   365   \item \isa {max} (constant), 23, 24
       
   366   \item measure functions, 47, 114
       
   367   \item \isa {measure_def} (theorem), \bold{115}
       
   368   \item meta-logic, \bold{80}
       
   369   \item methods, \bold{16}
       
   370   \item \isa {min} (constant), 23, 24
       
   371   \item mixfix annotations, \bold{53}
       
   372   \item \isa {mod} (symbol), 23
       
   373   \item \isa {mod_div_equality} (theorem), \bold{151}
       
   374   \item \isa {mod_mult_distrib} (theorem), \bold{151}
       
   375   \item model checking example, 116--126
       
   376   \item \emph{modus ponens}, 67, 72
       
   377   \item \isa {mono_def} (theorem), \bold{116}
       
   378   \item monotone functions, \bold{116}, 139
       
   379     \subitem and inductive definitions, 137--138
       
   380   \item \isa {more} (constant), 159, 160
       
   381   \item \isa {mp} (theorem), \bold{72}
       
   382   \item \isa {mult_ac} (theorems), 152
       
   383   \item multiple inheritance, \bold{170}
       
   384   \item multiset ordering, \bold{115}
       
   385 
       
   386   \indexspace
       
   387 
       
   388   \item \isa {nat} (type), 4, 22, 151--153
       
   389   \item \isa {nat_less_induct} (theorem), 188
       
   390   \item natural deduction, 67--68
       
   391   \item natural numbers, 22, 151--153
       
   392   \item Needham-Schroeder protocol, 195--197
       
   393   \item negation, 73--75
       
   394   \item \isa {Nil} (constant), 9
       
   395   \item \isa {no_asm} (modifier), 29
       
   396   \item \isa {no_asm_simp} (modifier), 30
       
   397   \item \isa {no_asm_use} (modifier), 30
       
   398   \item \isa {no_vars} (attribute), 62
       
   399   \item non-standard reals, 155
       
   400   \item \isa {None} (constant), \bold{24}
       
   401   \item \isa {notE} (theorem), \bold{73}
       
   402   \item \isa {notI} (theorem), \bold{73}
       
   403   \item numbers, 149--155
       
   404   \item numeric literals, 150
       
   405     \subitem for type \protect\isa{nat}, 151
       
   406     \subitem for type \protect\isa{real}, 155
       
   407 
       
   408   \indexspace
       
   409 
       
   410   \item \isa {O} (symbol), 112
       
   411   \item \texttt {o}, \bold{209}
       
   412   \item \isa {o_def} (theorem), \bold{110}
       
   413   \item \isa {OF} (attribute), 95--96
       
   414   \item \isa {of} (attribute), 93, 96
       
   415   \item \isa {only} (modifier), 29
       
   416   \item \isacommand {oops} (command), 13
       
   417   \item \isa {option} (type), \bold{24}
       
   418   \item ordered rewriting, \bold{176}
       
   419   \item overloading, 23, 165--167
       
   420     \subitem and arithmetic, 150
       
   421 
       
   422   \indexspace
       
   423 
       
   424   \item pairs and tuples, 24, 155--158
       
   425   \item parent theories, \bold{4}
       
   426   \item pattern matching
       
   427     \subitem and \isacommand{recdef}, 47
       
   428   \item patterns
       
   429     \subitem higher-order, \bold{177}
       
   430   \item PDL, 118--120
       
   431   \item \isacommand {pr} (command), 16, 100
       
   432   \item \isacommand {prefer} (command), 16, 101
       
   433   \item prefix annotation, 55
       
   434   \item primitive recursion, \see{recursion, primitive}{1}
       
   435   \item \isacommand {primrec} (command), 10, 18, 38--44
       
   436   \item print mode, \bold{55}
       
   437   \item product type, \see{pairs and tuples}{1}
       
   438   \item Proof General, \bold{7}
       
   439   \item proof state, 12
       
   440   \item proofs
       
   441     \subitem abandoning, \bold{13}
       
   442     \subitem examples of failing, 88--89
       
   443   \item protocols
       
   444     \subitem security, 195--205
       
   445 
       
   446   \indexspace
       
   447 
       
   448   \item quantifiers, 6
       
   449     \subitem and inductive definitions, 135--137
       
   450     \subitem existential, 82--83
       
   451     \subitem for sets, 108
       
   452     \subitem instantiating, 84
       
   453     \subitem universal, 80--82
       
   454 
       
   455   \indexspace
       
   456 
       
   457   \item \isa {r_into_rtrancl} (theorem), \bold{112}
       
   458   \item \isa {r_into_trancl} (theorem), \bold{113}
       
   459   \item range
       
   460     \subitem of a function, 111
       
   461     \subitem of a relation, 112
       
   462   \item \isa {range} (symbol), 111
       
   463   \item \isa {Range_iff} (theorem), \bold{112}
       
   464   \item \isa {Real} (theory), 155
       
   465   \item \isa {real} (type), 154--155
       
   466   \item real numbers, 154--155
       
   467   \item \isacommand {recdef} (command), 47--52, 114, 178--186
       
   468     \subitem and numeric literals, 150
       
   469   \item \isa {recdef_cong} (attribute), 182
       
   470   \item \isa {recdef_simp} (attribute), 49
       
   471   \item \isa {recdef_wf} (attribute), 180
       
   472   \item \isacommand {record} (command), 159
       
   473   \item records, 158--164
       
   474     \subitem extensible, 160--161
       
   475   \item recursion
       
   476     \subitem guarded, 183
       
   477     \subitem primitive, 18
       
   478     \subitem well-founded, \bold{179}
       
   479   \item recursion induction, 51--52
       
   480   \item \isacommand {redo} (command), 16
       
   481   \item reflexive and transitive closure, 112--114
       
   482   \item reflexive transitive closure
       
   483     \subitem defining inductively, 132--135
       
   484   \item \isa {rel_comp_def} (theorem), \bold{112}
       
   485   \item relations, 111--114
       
   486     \subitem well-founded, 114--115
       
   487   \item \isa {rename_tac} (method), 83
       
   488   \item \isa {rev} (constant), 10--14, 34
       
   489   \item rewrite rules, \bold{27}
       
   490     \subitem permutative, \bold{176}
       
   491   \item rewriting, \bold{27}
       
   492   \item \isa {rtrancl_refl} (theorem), \bold{112}
       
   493   \item \isa {rtrancl_trans} (theorem), \bold{112}
       
   494   \item rule induction, 128--130
       
   495   \item rule inversion, 130--131, 139--140
       
   496   \item \isa {rule_format} (attribute), 187
       
   497   \item \isa {rule_tac} (method), 76
       
   498     \subitem and renaming, 83
       
   499 
       
   500   \indexspace
       
   501 
       
   502   \item \isa {safe} (method), 91, 92
       
   503   \item safe rules, \bold{90}
       
   504   \item \isacommand {sect} (command), 59
       
   505   \item \isacommand {section} (command), 59
       
   506   \item selector
       
   507     \subitem record, 159
       
   508   \item session, \bold{58}
       
   509   \item \isa {set} (type), 5, 105
       
   510   \item set comprehensions, 107--108
       
   511   \item \isa {set_ext} (theorem), \bold{106}
       
   512   \item sets, 105--109
       
   513     \subitem finite, 109
       
   514     \subitem notation for finite, \bold{107}
       
   515   \item settings, \see{flags}{1}
       
   516   \item \isa {show_brackets} (flag), 6
       
   517   \item \isa {show_types} (flag), 5, 16
       
   518   \item \isa {simp} (attribute), 11, 28
       
   519   \item \isa {simp} (method), \bold{28}
       
   520   \item \isa {simp} del (attribute), 28
       
   521   \item \isa {simp_all} (method), 29, 38
       
   522   \item simplification, 27--33, 175--178
       
   523     \subitem of \isa{let}-expressions, 31
       
   524     \subitem with definitions, 30
       
   525     \subitem with/of assumptions, 29
       
   526   \item simplification rule, 177--178
       
   527   \item simplification rules, 28
       
   528     \subitem adding and deleting, 29
       
   529   \item \isa {simplified} (attribute), 94, 96
       
   530   \item \isa {size} (constant), 17
       
   531   \item \isa {snd} (constant), 24
       
   532   \item \isa {SOME} (symbol), 86
       
   533   \item \texttt {SOME}, \bold{209}
       
   534   \item \isa {Some} (constant), \bold{24}
       
   535   \item \isa {some_equality} (theorem), \bold{87}
       
   536   \item \isa {someI} (theorem), \bold{87}
       
   537   \item \isa {someI2} (theorem), \bold{87}
       
   538   \item \isa {someI_ex} (theorem), \bold{87}
       
   539   \item sorts, 170
       
   540   \item source comments, \bold{60}
       
   541   \item \isa {spec} (theorem), \bold{81}
       
   542   \item \isa {split} (attribute), 32
       
   543   \item \isa {split} (constant), 156
       
   544   \item \isa {split} (method), 31, 156
       
   545   \item \isa {split} (modifier), 32
       
   546   \item split rule, \bold{32}
       
   547   \item \isa {split_if} (theorem), 32
       
   548   \item \isa {split_if_asm} (theorem), 32
       
   549   \item \isa {ssubst} (theorem), \bold{77}
       
   550   \item structural induction, \see{induction, structural}{1}
       
   551   \item subclasses, 165, 169
       
   552   \item subgoal numbering, 46
       
   553   \item \isa {subgoal_tac} (method), 98, 99
       
   554   \item subgoals, 12
       
   555   \item \isacommand {subsect} (command), 59
       
   556   \item \isacommand {subsection} (command), 59
       
   557   \item subset relation, \bold{106}
       
   558   \item \isa {subsetD} (theorem), \bold{106}
       
   559   \item \isa {subsetI} (theorem), \bold{106}
       
   560   \item \isa {subst} (method), 77
       
   561   \item substitution, 77--80
       
   562   \item \isacommand {subsubsect} (command), 59
       
   563   \item \isacommand {subsubsection} (command), 59
       
   564   \item \isa {Suc} (constant), 22
       
   565   \item \isa {surj_def} (theorem), \bold{110}
       
   566   \item surjections, 110
       
   567   \item \isa {sym} (theorem), \bold{94}
       
   568   \item symbols, \bold{54}
       
   569   \item syntax, 6, 11
       
   570   \item \isacommand {syntax} (command), 55
       
   571   \item syntax (command), 56
       
   572   \item syntax translations, \bold{56}
       
   573 
       
   574   \indexspace
       
   575 
       
   576   \item tacticals, 99--100
       
   577   \item tactics, 12
       
   578   \item \isacommand {term} (command), 16
       
   579   \item term rewriting, \bold{27}
       
   580   \item termination, \see{functions, total}{1}
       
   581   \item terms, 5
       
   582   \item text, \bold{61}
       
   583   \item text blocks, \bold{61}
       
   584   \item \isa {THE} (symbol), 85
       
   585   \item \isa {the_equality} (theorem), \bold{86}
       
   586   \item \isa {THEN} (attribute), \bold{94}, 96, 103
       
   587   \item \isacommand {theorem} (command), \bold{11}, 13
       
   588   \item theories, 4
       
   589     \subitem abandoning, \bold{16}
       
   590   \item \isacommand {theory} (command), 16
       
   591   \item theory files, 4
       
   592   \item \isacommand {thm} (command), 16
       
   593   \item \isa {tl} (constant), 17
       
   594   \item \isa {ToyList} example, 9--14
       
   595   \item \isa {trace_simp} (flag), 33
       
   596   \item tracing the simplifier, \bold{33}
       
   597   \item \isa {trancl_trans} (theorem), \bold{113}
       
   598   \item transition systems, 117
       
   599   \item \isacommand {translations} (command), 56
       
   600   \item tries, 44--46
       
   601   \item \isa {True} (constant), 5
       
   602   \item \isa {truncate} (constant), 163
       
   603   \item tuples, \see{pairs and tuples}{1}
       
   604   \item txt, \bold{61}
       
   605   \item \isacommand {typ} (command), 16
       
   606   \item type constraints, \bold{6}
       
   607   \item type constructors, 5
       
   608   \item type inference, \bold{5}
       
   609   \item type synonyms, 25
       
   610   \item type variables, 5
       
   611   \item \isacommand {typedecl} (command), 117, 171
       
   612   \item \isacommand {typedef} (command), 172--174
       
   613   \item types, 4--5
       
   614     \subitem declaring, 171
       
   615     \subitem defining, 172--174
       
   616   \item \isacommand {types} (command), 25
       
   617 
       
   618   \indexspace
       
   619 
       
   620   \item Ullman, J. D., 145
       
   621   \item \texttt {UN}, \bold{209}
       
   622   \item \texttt {Un}, \bold{209}
       
   623   \item \isa {UN_E} (theorem), \bold{108}
       
   624   \item \isa {UN_I} (theorem), \bold{108}
       
   625   \item \isa {UN_iff} (theorem), \bold{108}
       
   626   \item \isa {Un_subset_iff} (theorem), \bold{106}
       
   627   \item \isacommand {undo} (command), 16
       
   628   \item \isa {unfold} (method), \bold{30}
       
   629   \item unification, 76--79
       
   630   \item \isa {UNION} (constant), 109
       
   631   \item \texttt {Union}, \bold{209}
       
   632   \item union
       
   633     \subitem indexed, 108
       
   634   \item \isa {Union_iff} (theorem), \bold{108}
       
   635   \item \isa {unit} (type), 24
       
   636   \item unknowns, 7, \bold{68}
       
   637   \item unsafe rules, \bold{90}
       
   638   \item update
       
   639     \subitem record, 159
       
   640   \item updating a function, \bold{109}
       
   641 
       
   642   \indexspace
       
   643 
       
   644   \item variables, 7
       
   645     \subitem schematic, 7
       
   646     \subitem type, 5
       
   647   \item \isa {vimage_def} (theorem), \bold{111}
       
   648 
       
   649   \indexspace
       
   650 
       
   651   \item \isa {wf_induct} (theorem), \bold{115}
       
   652   \item \isa {wf_inv_image} (theorem), \bold{115}
       
   653   \item \isa {wf_less_than} (theorem), \bold{114}
       
   654   \item \isa {wf_lex_prod} (theorem), \bold{115}
       
   655   \item \isa {wf_measure} (theorem), \bold{115}
       
   656   \item \isa {wf_subset} (theorem), 180
       
   657   \item \isa {while} (constant), 185
       
   658   \item \isa {While_Combinator} (theory), 185
       
   659   \item \isa {while_rule} (theorem), 185
       
   660 
       
   661   \indexspace
       
   662 
       
   663   \item \isa {zadd_ac} (theorems), 153
       
   664   \item \isa {zmult_ac} (theorems), 153
       
   665 
       
   666 \end{theindex}