doc-src/TutorialI/tutorial.ind
changeset 13081 ab4a3aef3591
parent 12821 ed702a3af45c
child 13111 2d6782e71702
equal deleted inserted replaced
13080:d9feada9c486 13081:ab4a3aef3591
     8   \item \verb$~$, \bold{209}
     8   \item \verb$~$, \bold{209}
     9   \item \verb$~=$, \bold{209}
     9   \item \verb$~=$, \bold{209}
    10   \item \ttor, \bold{209}
    10   \item \ttor, \bold{209}
    11   \item \texttt{[]}, \bold{9}
    11   \item \texttt{[]}, \bold{9}
    12   \item \texttt{\#}, \bold{9}
    12   \item \texttt{\#}, \bold{9}
    13   \item \texttt{\at}, \bold{10}, 209
    13   \item \texttt{\at}, \bold{10}, \hyperpage{209}
    14   \item \isasymnotin, \bold{209}
    14   \item \isasymnotin, \bold{209}
    15   \item \verb$~:$, \bold{209}
    15   \item \verb$~:$, \bold{209}
    16   \item \isasymInter, \bold{209}
    16   \item \isasymInter, \bold{209}
    17   \item \isasymUnion, \bold{209}
    17   \item \isasymUnion, \bold{209}
    18   \item \isasyminverse, \bold{209}
    18   \item \isasyminverse, \bold{209}
    24   \item \emph {$\Rightarrow $}, \bold{5}
    24   \item \emph {$\Rightarrow $}, \bold{5}
    25   \item \ttlbr, \bold{209}
    25   \item \ttlbr, \bold{209}
    26   \item \ttrbr, \bold{209}
    26   \item \ttrbr, \bold{209}
    27   \item \texttt {\%}, \bold{209}
    27   \item \texttt {\%}, \bold{209}
    28   \item \texttt {;}, \bold{7}
    28   \item \texttt {;}, \bold{7}
    29   \item \isa {()} (constant), 24
    29   \item \isa {()} (constant), \hyperpage{24}
    30   \item \isa {+} (tactical), 99
    30   \item \isa {+} (tactical), \hyperpage{99}
    31   \item \isa {<*lex*>}, \see{lexicographic product}{1}
    31   \item \isa {<*lex*>}, \see{lexicographic product}{1}
    32   \item \isa {?} (tactical), 99
    32   \item \isa {?} (tactical), \hyperpage{99}
    33   \item \texttt{|} (tactical), 99
    33   \item \texttt{|} (tactical), \hyperpage{99}
    34 
    34 
    35   \indexspace
    35   \indexspace
    36 
    36 
    37   \item \isa {0} (constant), 22, 23, 150
    37   \item \isa {0} (constant), \hyperpage{22, 23}, \hyperpage{150}
    38   \item \isa {1} (constant), 23, 150, 151
    38   \item \isa {1} (constant), \hyperpage{23}, \hyperpage{150, 151}
    39 
    39 
    40   \indexspace
    40   \indexspace
    41 
    41 
    42   \item abandoning a proof, \bold{13}
    42   \item abandoning a proof, \bold{13}
    43   \item abandoning a theory, \bold{16}
    43   \item abandoning a theory, \bold{16}
    44   \item \isa {abs} (constant), 153
    44   \item \isa {abs} (constant), \hyperpage{153}
    45   \item \texttt {abs}, \bold{209}
    45   \item \texttt {abs}, \bold{209}
    46   \item absolute value, 153
    46   \item absolute value, \hyperpage{153}
    47   \item \isa {add} (modifier), 29
    47   \item \isa {add} (modifier), \hyperpage{29}
    48   \item \isa {add_ac} (theorems), 152
    48   \item \isa {add_ac} (theorems), \hyperpage{152}
    49   \item \isa {add_assoc} (theorem), \bold{152}
    49   \item \isa {add_assoc} (theorem), \bold{152}
    50   \item \isa {add_commute} (theorem), \bold{152}
    50   \item \isa {add_commute} (theorem), \bold{152}
    51   \item \isa {add_mult_distrib} (theorem), \bold{151}
    51   \item \isa {add_mult_distrib} (theorem), \bold{151}
    52   \item \texttt {ALL}, \bold{209}
    52   \item \texttt {ALL}, \bold{209}
    53   \item \isa {All} (constant), 109
    53   \item \isa {All} (constant), \hyperpage{109}
    54   \item \isa {allE} (theorem), \bold{81}
    54   \item \isa {allE} (theorem), \bold{81}
    55   \item \isa {allI} (theorem), \bold{80}
    55   \item \isa {allI} (theorem), \bold{80}
    56   \item antiquotation, \bold{61}
    56   \item antiquotation, \bold{61}
    57   \item append function, 10--14
    57   \item append function, 10--14
    58   \item \isacommand {apply} (command), 15
    58   \item \isacommand {apply} (command), \hyperpage{15}
    59   \item \isa {arg_cong} (theorem), \bold{96}
    59   \item \isa {arg_cong} (theorem), \bold{96}
    60   \item \isa {arith} (method), 23, 149
    60   \item \isa {arith} (method), \hyperpage{23}, \hyperpage{149}
    61   \item arithmetic operations
    61   \item arithmetic operations
    62     \subitem for \protect\isa{nat}, 23
    62     \subitem for \protect\isa{nat}, \hyperpage{23}
    63   \item \textsc {ascii} symbols, \bold{209}
    63   \item \textsc {ascii} symbols, \bold{209}
    64   \item Aspinall, David, viii
    64   \item Aspinall, David, \hyperpage{viii}
    65   \item associative-commutative function, 176
    65   \item associative-commutative function, \hyperpage{176}
    66   \item \isa {assumption} (method), 69
    66   \item \isa {assumption} (method), \hyperpage{69}
    67   \item assumptions
    67   \item assumptions
    68     \subitem of subgoal, 12
    68     \subitem of subgoal, \hyperpage{12}
    69     \subitem renaming, 82--83
    69     \subitem renaming, 82--83
    70     \subitem reusing, 83
    70     \subitem reusing, 83
    71   \item \isa {auto} (method), 38, 92
    71   \item \isa {auto} (method), \hyperpage{38}, \hyperpage{92}
    72   \item \isa {axclass}, 164--170
    72   \item \isa {axclass}, 164--170
    73   \item axiom of choice, 86
    73   \item axiom of choice, \hyperpage{86}
    74   \item axiomatic type classes, 164--170
    74   \item axiomatic type classes, 164--170
    75 
    75 
    76   \indexspace
    76   \indexspace
    77 
    77 
    78   \item \isacommand {back} (command), 78
    78   \item \isacommand {back} (command), \hyperpage{78}
    79   \item \isa {Ball} (constant), 109
    79   \item \isa {Ball} (constant), \hyperpage{109}
    80   \item \isa {ballI} (theorem), \bold{108}
    80   \item \isa {ballI} (theorem), \bold{108}
    81   \item \isa {best} (method), 92
    81   \item \isa {best} (method), \hyperpage{92}
    82   \item \isa {Bex} (constant), 109
    82   \item \isa {Bex} (constant), \hyperpage{109}
    83   \item \isa {bexE} (theorem), \bold{108}
    83   \item \isa {bexE} (theorem), \bold{108}
    84   \item \isa {bexI} (theorem), \bold{108}
    84   \item \isa {bexI} (theorem), \bold{108}
    85   \item \isa {bij_def} (theorem), \bold{110}
    85   \item \isa {bij_def} (theorem), \bold{110}
    86   \item bijections, 110
    86   \item bijections, \hyperpage{110}
    87   \item binary trees, 18
    87   \item binary trees, \hyperpage{18}
    88   \item binomial coefficients, 109
    88   \item binomial coefficients, \hyperpage{109}
    89   \item bisimulations, 116
    89   \item bisimulations, \hyperpage{116}
    90   \item \isa {blast} (method), 89--90, 92
    90   \item \isa {blast} (method), 89--90, \hyperpage{92}
    91   \item \isa {bool} (type), 4, 5
    91   \item \isa {bool} (type), \hyperpage{4, 5}
    92   \item boolean expressions example, 20--22
    92   \item boolean expressions example, 20--22
    93   \item \isa {bspec} (theorem), \bold{108}
    93   \item \isa {bspec} (theorem), \bold{108}
    94   \item \isacommand{by} (command), 73
    94   \item \isacommand{by} (command), 73
    95 
    95 
    96   \indexspace
    96   \indexspace
    97 
    97 
    98   \item \isa {card} (constant), 109
    98   \item \isa {card} (constant), \hyperpage{109}
    99   \item \isa {card_Pow} (theorem), \bold{109}
    99   \item \isa {card_Pow} (theorem), \bold{109}
   100   \item \isa {card_Un_Int} (theorem), \bold{109}
   100   \item \isa {card_Un_Int} (theorem), \bold{109}
   101   \item cardinality, 109
   101   \item cardinality, \hyperpage{109}
   102   \item \isa {case} (symbol), 32, 33
   102   \item \isa {case} (symbol), \hyperpage{32, 33}
   103   \item \isa {case} expressions, 5, 6, 18
   103   \item \isa {case} expressions, \hyperpage{5, 6}, \hyperpage{18}
   104   \item case distinctions, 19
   104   \item case distinctions, \hyperpage{19}
   105   \item case splits, \bold{31}
   105   \item case splits, \bold{31}
   106   \item \isa {case_tac} (method), 19, 101, 157
   106   \item \isa {case_tac} (method), \hyperpage{19}, \hyperpage{101}, 
   107   \item \isa {cases} (method), 162
   107 		\hyperpage{157}
   108   \item \isacommand {chapter} (command), 59
   108   \item \isa {cases} (method), \hyperpage{162}
   109   \item \isa {clarify} (method), 91, 92
   109   \item \isacommand {chapter} (command), \hyperpage{59}
   110   \item \isa {clarsimp} (method), 91, 92
   110   \item \isa {clarify} (method), \hyperpage{91, 92}
       
   111   \item \isa {clarsimp} (method), \hyperpage{91, 92}
   111   \item \isa {classical} (theorem), \bold{73}
   112   \item \isa {classical} (theorem), \bold{73}
   112   \item coinduction, \bold{116}
   113   \item coinduction, \bold{116}
   113   \item \isa {Collect} (constant), 109
   114   \item \isa {Collect} (constant), \hyperpage{109}
   114   \item compiling expressions example, 36--38
   115   \item compiling expressions example, 36--38
   115   \item \isa {Compl_iff} (theorem), \bold{106}
   116   \item \isa {Compl_iff} (theorem), \bold{106}
   116   \item complement
   117   \item complement
   117     \subitem of a set, 105
   118     \subitem of a set, \hyperpage{105}
   118   \item composition
   119   \item composition
   119     \subitem of functions, \bold{110}
   120     \subitem of functions, \bold{110}
   120     \subitem of relations, \bold{112}
   121     \subitem of relations, \bold{112}
   121   \item conclusion
   122   \item conclusion
   122     \subitem of subgoal, 12
   123     \subitem of subgoal, \hyperpage{12}
   123   \item conditional expressions, \see{\isa{if} expressions}{1}
   124   \item conditional expressions, \see{\isa{if} expressions}{1}
   124   \item conditional simplification rules, 31
   125   \item conditional simplification rules, \hyperpage{31}
   125   \item \isa {cong} (attribute), 176
   126   \item \isa {cong} (attribute), \hyperpage{176}
   126   \item congruence rules, \bold{175}
   127   \item congruence rules, \bold{175}
   127   \item \isa {conjE} (theorem), \bold{71}
   128   \item \isa {conjE} (theorem), \bold{71}
   128   \item \isa {conjI} (theorem), \bold{68}
   129   \item \isa {conjI} (theorem), \bold{68}
   129   \item \isa {Cons} (constant), 9
   130   \item \isa {Cons} (constant), \hyperpage{9}
   130   \item \isacommand {constdefs} (command), 25
   131   \item \isacommand {constdefs} (command), \hyperpage{25}
   131   \item \isacommand {consts} (command), 10
   132   \item \isacommand {consts} (command), \hyperpage{10}
   132   \item contrapositives, 73
   133   \item contrapositives, 73
   133   \item converse
   134   \item converse
   134     \subitem of a relation, \bold{112}
   135     \subitem of a relation, \bold{112}
   135   \item \isa {converse_iff} (theorem), \bold{112}
   136   \item \isa {converse_iff} (theorem), \bold{112}
   136   \item CTL, 121--126, 191--193
   137   \item CTL, 121--126, 191--193
   137 
   138 
   138   \indexspace
   139   \indexspace
   139 
   140 
   140   \item \isacommand {datatype} (command), 9, 38--43
   141   \item \isacommand {datatype} (command), \hyperpage{9}, 38--43
   141   \item datatypes, 17--22
   142   \item datatypes, 17--22
   142     \subitem and nested recursion, 40, 44
   143     \subitem and nested recursion, \hyperpage{40}, \hyperpage{44}
   143     \subitem mutually recursive, 38
   144     \subitem mutually recursive, \hyperpage{38}
   144     \subitem nested, 180
   145     \subitem nested, \hyperpage{180}
   145   \item \isacommand {defer} (command), 16, 100
   146   \item \isacommand {defer} (command), \hyperpage{16}, \hyperpage{100}
   146   \item Definitional Approach, 26
   147   \item Definitional Approach, \hyperpage{26}
   147   \item definitions, \bold{25}
   148   \item definitions, \bold{25}
   148     \subitem unfolding, \bold{30}
   149     \subitem unfolding, \bold{30}
   149   \item \isacommand {defs} (command), 25
   150   \item \isacommand {defs} (command), \hyperpage{25}
   150   \item \isa {del} (modifier), 29
   151   \item \isa {del} (modifier), \hyperpage{29}
   151   \item description operators, 85--87
   152   \item description operators, 85--87
   152   \item descriptions
   153   \item descriptions
   153     \subitem definite, 85
   154     \subitem definite, \hyperpage{85}
   154     \subitem indefinite, 86
   155     \subitem indefinite, \hyperpage{86}
   155   \item \isa {dest} (attribute), 102
   156   \item \isa {dest} (attribute), \hyperpage{102}
   156   \item destruction rules, 71
   157   \item destruction rules, 71
   157   \item \isa {diff_mult_distrib} (theorem), \bold{151}
   158   \item \isa {diff_mult_distrib} (theorem), \bold{151}
   158   \item difference
   159   \item difference
   159     \subitem of sets, \bold{106}
   160     \subitem of sets, \bold{106}
   160   \item \isa {disjCI} (theorem), \bold{74}
   161   \item \isa {disjCI} (theorem), \bold{74}
   161   \item \isa {disjE} (theorem), \bold{70}
   162   \item \isa {disjE} (theorem), \bold{70}
   162   \item \isa {div} (symbol), 23
   163   \item \isa {div} (symbol), \hyperpage{23}
   163   \item divides relation, 84, 95, 101--104, 152
   164   \item divides relation, \hyperpage{84}, \hyperpage{95}, 101--104, 
       
   165 		\hyperpage{152}
   164   \item division
   166   \item division
   165     \subitem by negative numbers, 153
   167     \subitem by negative numbers, \hyperpage{153}
   166     \subitem by zero, 152
   168     \subitem by zero, \hyperpage{152}
   167     \subitem for type \protect\isa{nat}, 151
   169     \subitem for type \protect\isa{nat}, \hyperpage{151}
   168   \item documents, \bold{57}
   170   \item documents, \bold{57}
   169   \item domain
   171   \item domain
   170     \subitem of a relation, 112
   172     \subitem of a relation, \hyperpage{112}
   171   \item \isa {Domain_iff} (theorem), \bold{112}
   173   \item \isa {Domain_iff} (theorem), \bold{112}
   172   \item \isacommand {done} (command), 13
   174   \item \isacommand {done} (command), \hyperpage{13}
   173   \item \isa {drule_tac} (method), 76, 96
   175   \item \isa {drule_tac} (method), \hyperpage{76}, \hyperpage{96}
   174   \item \isa {dvd_add} (theorem), \bold{152}
   176   \item \isa {dvd_add} (theorem), \bold{152}
   175   \item \isa {dvd_anti_sym} (theorem), \bold{152}
   177   \item \isa {dvd_anti_sym} (theorem), \bold{152}
   176   \item \isa {dvd_def} (theorem), \bold{152}
   178   \item \isa {dvd_def} (theorem), \bold{152}
   177 
   179 
   178   \indexspace
   180   \indexspace
   179 
   181 
   180   \item \isa {elim!} (attribute), 131
   182   \item \isa {elim!} (attribute), \hyperpage{131}
   181   \item elimination rules, 69--70
   183   \item elimination rules, 69--70
   182   \item \isacommand {end} (command), 14
   184   \item \isacommand {end} (command), \hyperpage{14}
   183   \item \isa {Eps} (constant), 109
   185   \item \isa {Eps} (constant), \hyperpage{109}
   184   \item equality, 5
   186   \item equality, \hyperpage{5}
   185     \subitem of functions, \bold{109}
   187     \subitem of functions, \bold{109}
   186     \subitem of records, 161
   188     \subitem of records, \hyperpage{161}
   187     \subitem of sets, \bold{106}
   189     \subitem of sets, \bold{106}
   188   \item \isa {equalityE} (theorem), \bold{106}
   190   \item \isa {equalityE} (theorem), \bold{106}
   189   \item \isa {equalityI} (theorem), \bold{106}
   191   \item \isa {equalityI} (theorem), \bold{106}
   190   \item \isa {erule} (method), 70
   192   \item \isa {erule} (method), \hyperpage{70}
   191   \item \isa {erule_tac} (method), 76
   193   \item \isa {erule_tac} (method), \hyperpage{76}
   192   \item Euclid's algorithm, 101--104
   194   \item Euclid's algorithm, 101--104
   193   \item even numbers
   195   \item even numbers
   194     \subitem defining inductively, 127--131
   196     \subitem defining inductively, 127--131
   195   \item \texttt {EX}, \bold{209}
   197   \item \texttt {EX}, \bold{209}
   196   \item \isa {Ex} (constant), 109
   198   \item \isa {Ex} (constant), \hyperpage{109}
   197   \item \isa {exE} (theorem), \bold{82}
   199   \item \isa {exE} (theorem), \bold{82}
   198   \item \isa {exI} (theorem), \bold{82}
   200   \item \isa {exI} (theorem), \bold{82}
   199   \item \isa {ext} (theorem), \bold{109}
   201   \item \isa {ext} (theorem), \bold{109}
   200   \item \isa {extend} (constant), 163
   202   \item \isa {extend} (constant), \hyperpage{163}
   201   \item extensionality
   203   \item extensionality
   202     \subitem for functions, \bold{109, 110}
   204     \subitem for functions, \bold{109, 110}
   203     \subitem for records, 162
   205     \subitem for records, \hyperpage{162}
   204     \subitem for sets, \bold{106}
   206     \subitem for sets, \bold{106}
   205   \item \ttEXU, \bold{209}
   207   \item \ttEXU, \bold{209}
   206 
   208 
   207   \indexspace
   209   \indexspace
   208 
   210 
   209   \item \isa {False} (constant), 5
   211   \item \isa {False} (constant), \hyperpage{5}
   210   \item \isa {fast} (method), 92, 124
   212   \item \isa {fast} (method), \hyperpage{92}, \hyperpage{124}
   211   \item Fibonacci function, 47
   213   \item Fibonacci function, \hyperpage{47}
   212   \item \isa {fields} (constant), 163
   214   \item \isa {fields} (constant), \hyperpage{163}
   213   \item \isa {finite} (symbol), 109
   215   \item \isa {finite} (symbol), \hyperpage{109}
   214   \item \isa {Finites} (constant), 109
   216   \item \isa {Finites} (constant), \hyperpage{109}
   215   \item fixed points, 116
   217   \item fixed points, 116
   216   \item flags, 5, 6, 33
   218   \item flags, \hyperpage{5, 6}, \hyperpage{33}
   217     \subitem setting and resetting, 5
   219     \subitem setting and resetting, \hyperpage{5}
   218   \item \isa {force} (method), 91, 92
   220   \item \isa {force} (method), \hyperpage{91, 92}
   219   \item formal comments, \bold{61}
   221   \item formal comments, \bold{61}
   220   \item formal proof documents, \bold{57}
   222   \item formal proof documents, \bold{57}
   221   \item formulae, 5--6
   223   \item formulae, 5--6
   222   \item forward proof, 92--98
   224   \item forward proof, 92--98
   223   \item \isa {frule} (method), 83
   225   \item \isa {frule} (method), 83
   224   \item \isa {frule_tac} (method), 76
   226   \item \isa {frule_tac} (method), \hyperpage{76}
   225   \item \isa {fst} (constant), 24
   227   \item \isa {fst} (constant), \hyperpage{24}
   226   \item function types, 5
   228   \item function types, \hyperpage{5}
   227   \item functions, 109--111
   229   \item functions, 109--111
   228     \subitem partial, 182
   230     \subitem partial, \hyperpage{182}
   229     \subitem total, 11, 46--52
   231     \subitem total, \hyperpage{11}, 47--52
   230     \subitem underdefined, 183
   232     \subitem underdefined, \hyperpage{183}
   231 
   233 
   232   \indexspace
   234   \indexspace
   233 
   235 
   234   \item \isa {gcd} (constant), 93--94, 101--104
   236   \item \isa {gcd} (constant), 93--94, 101--104
   235   \item generalizing for induction, 129
   237   \item generalizing for induction, \hyperpage{129}
   236   \item generalizing induction formulae, 35
   238   \item generalizing induction formulae, \hyperpage{35}
   237   \item Girard, Jean-Yves, \fnote{71}
   239   \item Girard, Jean-Yves, \fnote{71}
   238   \item Gordon, Mike, 3
   240   \item Gordon, Mike, \hyperpage{3}
   239   \item grammars
   241   \item grammars
   240     \subitem defining inductively, 140--145
   242     \subitem defining inductively, 140--145
   241   \item ground terms example, 135--140
   243   \item ground terms example, 135--140
   242 
   244 
   243   \indexspace
   245   \indexspace
   244 
   246 
   245   \item \isa {hd} (constant), 17, 37
   247   \item \isa {hd} (constant), \hyperpage{17}, \hyperpage{37}
   246   \item \isacommand {header} (command), 59
   248   \item \isacommand {header} (command), \hyperpage{59}
   247   \item Hilbert's $\varepsilon$-operator, 86
   249   \item Hilbert's $\varepsilon$-operator, \hyperpage{86}
   248   \item HOLCF, 43
   250   \item HOLCF, \hyperpage{43}
   249   \item Hopcroft, J. E., 145
   251   \item Hopcroft, J. E., \hyperpage{145}
   250   \item \isa {hypreal} (type), 155
   252   \item \isa {hypreal} (type), \hyperpage{155}
   251 
   253 
   252   \indexspace
   254   \indexspace
   253 
   255 
   254   \item \isa {Id_def} (theorem), \bold{112}
   256   \item \isa {Id_def} (theorem), \bold{112}
   255   \item \isa {id_def} (theorem), \bold{110}
   257   \item \isa {id_def} (theorem), \bold{110}
   256   \item identifiers, \bold{6}
   258   \item identifiers, \bold{6}
   257     \subitem qualified, \bold{4}
   259     \subitem qualified, \bold{4}
   258   \item identity function, \bold{110}
   260   \item identity function, \bold{110}
   259   \item identity relation, \bold{112}
   261   \item identity relation, \bold{112}
   260   \item \isa {if} expressions, 5, 6
   262   \item \isa {if} expressions, \hyperpage{5, 6}
   261     \subitem simplification of, 33
   263     \subitem simplification of, \hyperpage{33}
   262     \subitem splitting of, 31, 49
   264     \subitem splitting of, \hyperpage{31}, \hyperpage{49}
   263   \item if-and-only-if, 6
   265   \item if-and-only-if, \hyperpage{6}
   264   \item \isa {iff} (attribute), 90, 102, 130
   266   \item \isa {iff} (attribute), \hyperpage{90}, \hyperpage{102}, 
       
   267 		\hyperpage{130}
   265   \item \isa {iffD1} (theorem), \bold{94}
   268   \item \isa {iffD1} (theorem), \bold{94}
   266   \item \isa {iffD2} (theorem), \bold{94}
   269   \item \isa {iffD2} (theorem), \bold{94}
   267   \item ignored material, \bold{64}
   270   \item ignored material, \bold{64}
   268   \item image
   271   \item image
   269     \subitem under a function, \bold{111}
   272     \subitem under a function, \bold{111}
   270     \subitem under a relation, \bold{112}
   273     \subitem under a relation, \bold{112}
   271   \item \isa {image_def} (theorem), \bold{111}
   274   \item \isa {image_def} (theorem), \bold{111}
   272   \item \isa {Image_iff} (theorem), \bold{112}
   275   \item \isa {Image_iff} (theorem), \bold{112}
   273   \item \isa {impI} (theorem), \bold{72}
   276   \item \isa {impI} (theorem), \bold{72}
   274   \item implication, 72--73
   277   \item implication, 72--73
   275   \item \isa {ind_cases} (method), 131
   278   \item \isa {ind_cases} (method), \hyperpage{131}
   276   \item \isa {induct_tac} (method), 12, 19, 52, 190
   279   \item \isa {induct_tac} (method), \hyperpage{12}, \hyperpage{19}, 
       
   280 		\hyperpage{52}, \hyperpage{190}
   277   \item induction, 186--193
   281   \item induction, 186--193
   278     \subitem complete, 188
   282     \subitem complete, \hyperpage{188}
   279     \subitem deriving new schemas, 190
   283     \subitem deriving new schemas, \hyperpage{190}
   280     \subitem on a term, 187
   284     \subitem on a term, \hyperpage{187}
   281     \subitem recursion, 51--52
   285     \subitem recursion, 51--52
   282     \subitem structural, 19
   286     \subitem structural, \hyperpage{19}
   283     \subitem well-founded, 115
   287     \subitem well-founded, 115
   284   \item induction heuristics, 34--36
   288   \item induction heuristics, 34--36
   285   \item \isacommand {inductive} (command), 127
   289   \item \isacommand {inductive} (command), \hyperpage{127}
   286   \item inductive definition
   290   \item inductive definition
   287     \subitem simultaneous, 141
   291     \subitem simultaneous, \hyperpage{141}
   288   \item inductive definitions, 127--145
   292   \item inductive definitions, 127--145
   289   \item \isacommand {inductive\_cases} (command), 131, 139
   293   \item \isacommand {inductive\_cases} (command), \hyperpage{131}, 
   290   \item infinitely branching trees, 43
   294 		\hyperpage{139}
   291   \item infix annotations, 53
   295   \item infinitely branching trees, \hyperpage{43}
   292   \item \isacommand{infixr} (annotation), 10
   296   \item infix annotations, \hyperpage{53}
       
   297   \item \isacommand{infixr} (annotation), \hyperpage{10}
   293   \item \isa {inj_on_def} (theorem), \bold{110}
   298   \item \isa {inj_on_def} (theorem), \bold{110}
   294   \item injections, 110
   299   \item injections, \hyperpage{110}
   295   \item \isa {insert} (constant), 107
   300   \item \isa {insert} (constant), \hyperpage{107}
   296   \item \isa {insert} (method), 97--98
   301   \item \isa {insert} (method), \hyperpage{97}, 97, \hyperpage{98}
   297   \item instance, \bold{166}
   302   \item instance, \bold{166}
   298   \item \texttt {INT}, \bold{209}
   303   \item \texttt {INT}, \bold{209}
   299   \item \texttt {Int}, \bold{209}
   304   \item \texttt {Int}, \bold{209}
   300   \item \isa {int} (type), 153--154
   305   \item \isa {int} (type), 153--154
   301   \item \isa {INT_iff} (theorem), \bold{108}
   306   \item \isa {INT_iff} (theorem), \bold{108}
   302   \item \isa {IntD1} (theorem), \bold{105}
   307   \item \isa {IntD1} (theorem), \bold{105}
   303   \item \isa {IntD2} (theorem), \bold{105}
   308   \item \isa {IntD2} (theorem), \bold{105}
   304   \item integers, 153--154
   309   \item integers, 153--154
   305   \item \isa {INTER} (constant), 109
   310   \item \isa {INTER} (constant), \hyperpage{109}
   306   \item \texttt {Inter}, \bold{209}
   311   \item \texttt {Inter}, \bold{209}
   307   \item \isa {Inter_iff} (theorem), \bold{108}
   312   \item \isa {Inter_iff} (theorem), \bold{108}
   308   \item intersection, 105
   313   \item intersection, \hyperpage{105}
   309     \subitem indexed, 108
   314     \subitem indexed, \hyperpage{108}
   310   \item \isa {IntI} (theorem), \bold{105}
   315   \item \isa {IntI} (theorem), \bold{105}
   311   \item \isa {intro} (method), 74
   316   \item \isa {intro} (method), \hyperpage{74}
   312   \item \isa {intro!} (attribute), 128
   317   \item \isa {intro!} (attribute), \hyperpage{128}
   313   \item \isa {intro_classes} (method), 166
   318   \item \isa {intro_classes} (method), \hyperpage{166}
   314   \item introduction rules, 68--69
   319   \item introduction rules, 68--69
   315   \item \isa {inv} (constant), 86
   320   \item \isa {inv} (constant), \hyperpage{86}
   316   \item \isa {inv_image_def} (theorem), \bold{115}
   321   \item \isa {inv_image_def} (theorem), \bold{115}
   317   \item inverse
   322   \item inverse
   318     \subitem of a function, \bold{110}
   323     \subitem of a function, \bold{110}
   319     \subitem of a relation, \bold{112}
   324     \subitem of a relation, \bold{112}
   320   \item inverse image
   325   \item inverse image
   321     \subitem of a function, 111
   326     \subitem of a function, \hyperpage{111}
   322     \subitem of a relation, 114
   327     \subitem of a relation, \hyperpage{114}
   323   \item \isa {itrev} (constant), 34
   328   \item \isa {itrev} (constant), \hyperpage{34}
   324 
   329 
   325   \indexspace
   330   \indexspace
   326 
   331 
   327   \item \isacommand {kill} (command), 16
   332   \item \isacommand {kill} (command), \hyperpage{16}
   328 
   333 
   329   \indexspace
   334   \indexspace
   330 
   335 
   331   \item $\lambda$ expressions, 5
   336   \item $\lambda$ expressions, \hyperpage{5}
   332   \item LCF, 43
   337   \item LCF, \hyperpage{43}
   333   \item \isa {LEAST} (symbol), 23, 85
   338   \item \isa {LEAST} (symbol), \hyperpage{23}, \hyperpage{85}
   334   \item least number operator, \see{\protect\isa{LEAST}}{85}
   339   \item least number operator, \see{\protect\isa{LEAST}}{85}
   335   \item Leibniz, Gottfried Wilhelm, 53
   340   \item Leibniz, Gottfried Wilhelm, \hyperpage{53}
   336   \item \isacommand {lemma} (command), 13
   341   \item \isacommand {lemma} (command), \hyperpage{13}
   337   \item \isacommand {lemmas} (command), 93, 102
   342   \item \isacommand {lemmas} (command), \hyperpage{93}, \hyperpage{102}
   338   \item \isa {length} (symbol), 18
   343   \item \isa {length} (symbol), \hyperpage{18}
   339   \item \isa {length_induct}, \bold{190}
   344   \item \isa {length_induct}, \bold{190}
   340   \item \isa {less_than} (constant), 114
   345   \item \isa {less_than} (constant), \hyperpage{114}
   341   \item \isa {less_than_iff} (theorem), \bold{114}
   346   \item \isa {less_than_iff} (theorem), \bold{114}
   342   \item \isa {let} expressions, 5, 6, 31
   347   \item \isa {let} expressions, \hyperpage{5, 6}, \hyperpage{31}
   343   \item \isa {Let_def} (theorem), 31
   348   \item \isa {Let_def} (theorem), \hyperpage{31}
   344   \item \isa {lex_prod_def} (theorem), \bold{115}
   349   \item \isa {lex_prod_def} (theorem), \bold{115}
   345   \item lexicographic product, \bold{115}, 178
   350   \item lexicographic product, \bold{115}, \hyperpage{178}
   346   \item {\texttt{lfp}}
   351   \item {\texttt{lfp}}
   347     \subitem applications of, \see{CTL}{116}
   352     \subitem applications of, \see{CTL}{116}
   348   \item Library, 4
   353   \item Library, \hyperpage{4}
   349   \item linear arithmetic, 22--24, 149
   354   \item linear arithmetic, 22--24, \hyperpage{149}
   350   \item \isa {List} (theory), 17
   355   \item \isa {List} (theory), \hyperpage{17}
   351   \item \isa {list} (type), 5, 9, 17
   356   \item \isa {list} (type), \hyperpage{5}, \hyperpage{9}, 
   352   \item \isa {list.split} (theorem), 32
   357 		\hyperpage{17}
       
   358   \item \isa {list.split} (theorem), \hyperpage{32}
   353   \item \isa {lists_mono} (theorem), \bold{137}
   359   \item \isa {lists_mono} (theorem), \bold{137}
   354   \item Lowe, Gavin, 196--197
   360   \item Lowe, Gavin, 196--197
   355 
   361 
   356   \indexspace
   362   \indexspace
   357 
   363 
   358   \item \isa {Main} (theory), 4
   364   \item \isa {Main} (theory), \hyperpage{4}
   359   \item major premise, \bold{75}
   365   \item major premise, \bold{75}
   360   \item \isa {make} (constant), 163
   366   \item \isa {make} (constant), \hyperpage{163}
   361   \item marginal comments, \bold{61}
   367   \item marginal comments, \bold{61}
   362   \item markup commands, \bold{59}
   368   \item markup commands, \bold{59}
   363   \item \isa {max} (constant), 23, 24
   369   \item \isa {max} (constant), \hyperpage{23, 24}
   364   \item measure functions, 47, 114
   370   \item measure functions, \hyperpage{47}, \hyperpage{114}
   365   \item \isa {measure_def} (theorem), \bold{115}
   371   \item \isa {measure_def} (theorem), \bold{115}
   366   \item meta-logic, \bold{80}
   372   \item meta-logic, \bold{80}
   367   \item methods, \bold{16}
   373   \item methods, \bold{16}
   368   \item \isa {min} (constant), 23, 24
   374   \item \isa {min} (constant), \hyperpage{23, 24}
   369   \item mixfix annotations, \bold{53}
   375   \item mixfix annotations, \bold{53}
   370   \item \isa {mod} (symbol), 23
   376   \item \isa {mod} (symbol), \hyperpage{23}
   371   \item \isa {mod_div_equality} (theorem), \bold{151}
   377   \item \isa {mod_div_equality} (theorem), \bold{151}
   372   \item \isa {mod_mult_distrib} (theorem), \bold{151}
   378   \item \isa {mod_mult_distrib} (theorem), \bold{151}
   373   \item model checking example, 116--126
   379   \item model checking example, 116--126
   374   \item \emph{modus ponens}, 67, 72
   380   \item \emph{modus ponens}, \hyperpage{67}, \hyperpage{72}
   375   \item \isa {mono_def} (theorem), \bold{116}
   381   \item \isa {mono_def} (theorem), \bold{116}
   376   \item monotone functions, \bold{116}, 139
   382   \item monotone functions, \bold{116}, \hyperpage{139}
   377     \subitem and inductive definitions, 137--138
   383     \subitem and inductive definitions, 137--138
   378   \item \isa {more} (constant), 158, 160
   384   \item \isa {more} (constant), \hyperpage{158}, \hyperpage{160}
   379   \item \isa {mp} (theorem), \bold{72}
   385   \item \isa {mp} (theorem), \bold{72}
   380   \item \isa {mult_ac} (theorems), 152
   386   \item \isa {mult_ac} (theorems), \hyperpage{152}
   381   \item multiple inheritance, \bold{169}
   387   \item multiple inheritance, \bold{169}
   382   \item multiset ordering, \bold{115}
   388   \item multiset ordering, \bold{115}
   383 
   389 
   384   \indexspace
   390   \indexspace
   385 
   391 
   386   \item \isa {nat} (type), 4, 22, 151--153
   392   \item \isa {nat} (type), \hyperpage{4}, \hyperpage{22}, 151--153
   387   \item \isa {nat_less_induct} (theorem), 188
   393   \item \isa {nat_less_induct} (theorem), \hyperpage{188}
   388   \item natural deduction, 67--68
   394   \item natural deduction, 67--68
   389   \item natural numbers, 22, 151--153
   395   \item natural numbers, \hyperpage{22}, 151--153
   390   \item Needham-Schroeder protocol, 195--197
   396   \item Needham-Schroeder protocol, 195--197
   391   \item negation, 73--75
   397   \item negation, 73--75
   392   \item \isa {Nil} (constant), 9
   398   \item \isa {Nil} (constant), \hyperpage{9}
   393   \item \isa {no_asm} (modifier), 29
   399   \item \isa {no_asm} (modifier), \hyperpage{29}
   394   \item \isa {no_asm_simp} (modifier), 30
   400   \item \isa {no_asm_simp} (modifier), \hyperpage{30}
   395   \item \isa {no_asm_use} (modifier), 30
   401   \item \isa {no_asm_use} (modifier), \hyperpage{30}
   396   \item \isa {no_vars} (attribute), 62
   402   \item \isa {no_vars} (attribute), \hyperpage{62}
   397   \item non-standard reals, 155
   403   \item non-standard reals, \hyperpage{155}
   398   \item \isa {None} (constant), \bold{24}
   404   \item \isa {None} (constant), \bold{24}
   399   \item \isa {notE} (theorem), \bold{73}
   405   \item \isa {notE} (theorem), \bold{73}
   400   \item \isa {notI} (theorem), \bold{73}
   406   \item \isa {notI} (theorem), \bold{73}
   401   \item numbers, 149--155
   407   \item numbers, 149--155
   402   \item numeric literals, 150
   408   \item numeric literals, 150
   403     \subitem for type \protect\isa{nat}, 151
   409     \subitem for type \protect\isa{nat}, \hyperpage{151}
   404     \subitem for type \protect\isa{real}, 155
   410     \subitem for type \protect\isa{real}, \hyperpage{155}
   405 
   411 
   406   \indexspace
   412   \indexspace
   407 
   413 
   408   \item \isa {O} (symbol), 112
   414   \item \isa {O} (symbol), \hyperpage{112}
   409   \item \texttt {o}, \bold{209}
   415   \item \texttt {o}, \bold{209}
   410   \item \isa {o_def} (theorem), \bold{110}
   416   \item \isa {o_def} (theorem), \bold{110}
   411   \item \isa {OF} (attribute), 95--96
   417   \item \isa {OF} (attribute), 95--96, \hyperpage{96}
   412   \item \isa {of} (attribute), 93, 96
   418   \item \isa {of} (attribute), \hyperpage{93}, \hyperpage{96}
   413   \item \isa {only} (modifier), 29
   419   \item \isa {only} (modifier), \hyperpage{29}
   414   \item \isacommand {oops} (command), 13
   420   \item \isacommand {oops} (command), \hyperpage{13}
   415   \item \isa {option} (type), \bold{24}
   421   \item \isa {option} (type), \bold{24}
   416   \item ordered rewriting, \bold{176}
   422   \item ordered rewriting, \bold{176}
   417   \item overloading, 23, 165--167
   423   \item overloading, \hyperpage{23}, 165--167
   418     \subitem and arithmetic, 150
   424     \subitem and arithmetic, \hyperpage{150}
   419 
   425 
   420   \indexspace
   426   \indexspace
   421 
   427 
   422   \item pairs and tuples, 24, 155--158
   428   \item pairs and tuples, \hyperpage{24}, 155--158
   423   \item parent theories, \bold{4}
   429   \item parent theories, \bold{4}
   424   \item pattern matching
   430   \item pattern matching
   425     \subitem and \isacommand{recdef}, 47
   431     \subitem and \isacommand{recdef}, \hyperpage{47}
   426   \item patterns
   432   \item patterns
   427     \subitem higher-order, \bold{177}
   433     \subitem higher-order, \bold{177}
   428   \item PDL, 118--120
   434   \item PDL, 118--120
   429   \item \isacommand {pr} (command), 16, 100
   435   \item \isacommand {pr} (command), \hyperpage{16}, \hyperpage{100}
   430   \item \isacommand {prefer} (command), 16, 100
   436   \item \isacommand {prefer} (command), \hyperpage{16}, \hyperpage{100}
   431   \item prefix annotation, 55
   437   \item prefix annotation, \hyperpage{55}
   432   \item primitive recursion, \see{recursion, primitive}{1}
   438   \item primitive recursion, \see{recursion, primitive}{1}
   433   \item \isacommand {primrec} (command), 10, 18, 38--43
   439   \item \isacommand {primrec} (command), \hyperpage{10}, \hyperpage{18}, 
       
   440 		\hyperpage{41}, 38--43
   434   \item print mode, \bold{55}
   441   \item print mode, \bold{55}
   435   \item product type, \see{pairs and tuples}{1}
   442   \item product type, \see{pairs and tuples}{1}
   436   \item Proof General, \bold{7}
   443   \item Proof General, \bold{7}
   437   \item proof state, 12
   444   \item proof state, \hyperpage{12}
   438   \item proofs
   445   \item proofs
   439     \subitem abandoning, \bold{13}
   446     \subitem abandoning, \bold{13}
   440     \subitem examples of failing, 87--89
   447     \subitem examples of failing, 87--89
   441   \item protocols
   448   \item protocols
   442     \subitem security, 195--205
   449     \subitem security, 195--205
   443 
   450 
   444   \indexspace
   451   \indexspace
   445 
   452 
   446   \item quantifiers, 6
   453   \item quantifiers, \hyperpage{6}
   447     \subitem and inductive definitions, 135--137
   454     \subitem and inductive definitions, 135--137
   448     \subitem existential, 82
   455     \subitem existential, 82
   449     \subitem for sets, 108
   456     \subitem for sets, 108
   450     \subitem instantiating, 84
   457     \subitem instantiating, \hyperpage{84}
   451     \subitem universal, 79--82
   458     \subitem universal, 79--82
   452 
   459 
   453   \indexspace
   460   \indexspace
   454 
   461 
   455   \item \isa {r_into_rtrancl} (theorem), \bold{112}
   462   \item \isa {r_into_rtrancl} (theorem), \bold{112}
   456   \item \isa {r_into_trancl} (theorem), \bold{113}
   463   \item \isa {r_into_trancl} (theorem), \bold{113}
   457   \item range
   464   \item range
   458     \subitem of a function, 111
   465     \subitem of a function, \hyperpage{111}
   459     \subitem of a relation, 112
   466     \subitem of a relation, \hyperpage{112}
   460   \item \isa {range} (symbol), 111
   467   \item \isa {range} (symbol), \hyperpage{111}
   461   \item \isa {Range_iff} (theorem), \bold{112}
   468   \item \isa {Range_iff} (theorem), \bold{112}
   462   \item \isa {Real} (theory), 155
   469   \item \isa {Real} (theory), \hyperpage{155}
   463   \item \isa {real} (type), 154--155
   470   \item \isa {real} (type), 154--155
   464   \item real numbers, 154--155
   471   \item real numbers, 154--155
   465   \item \isacommand {recdef} (command), 46--52, 114, 178--186
   472   \item \isacommand {recdef} (command), 47--52, \hyperpage{114}, 
   466     \subitem and numeric literals, 150
   473 		178--186
   467   \item \isa {recdef_cong} (attribute), 182
   474     \subitem and numeric literals, \hyperpage{150}
   468   \item \isa {recdef_simp} (attribute), 49
   475   \item \isa {recdef_cong} (attribute), \hyperpage{182}
   469   \item \isa {recdef_wf} (attribute), 180
   476   \item \isa {recdef_simp} (attribute), \hyperpage{49}
   470   \item \isacommand {record} (command), 159
   477   \item \isa {recdef_wf} (attribute), \hyperpage{180}
       
   478   \item \isacommand {record} (command), \hyperpage{159}
   471   \item records, 158--164
   479   \item records, 158--164
   472     \subitem extensible, 160--161
   480     \subitem extensible, 160--161
   473   \item recursion
   481   \item recursion
   474     \subitem guarded, 183
   482     \subitem guarded, \hyperpage{183}
   475     \subitem primitive, 18
   483     \subitem primitive, \hyperpage{18}
   476     \subitem well-founded, \bold{179}
   484     \subitem well-founded, \bold{179}
   477   \item recursion induction, 51--52
   485   \item recursion induction, 51--52
   478   \item \isacommand {redo} (command), 16
   486   \item \isacommand {redo} (command), \hyperpage{16}
   479   \item reflexive and transitive closure, 112--114
   487   \item reflexive and transitive closure, 112--114
   480   \item reflexive transitive closure
   488   \item reflexive transitive closure
   481     \subitem defining inductively, 132--135
   489     \subitem defining inductively, 132--135
   482   \item \isa {rel_comp_def} (theorem), \bold{112}
   490   \item \isa {rel_comp_def} (theorem), \bold{112}
   483   \item relations, 111--114
   491   \item relations, 111--114
   484     \subitem well-founded, 114--115
   492     \subitem well-founded, 114--115
   485   \item \isa {rename_tac} (method), 82--83
   493   \item \isa {rename_tac} (method), 82--83
   486   \item \isa {rev} (constant), 10--14, 34
   494   \item \isa {rev} (constant), \hyperpage{10}, 10--14, \hyperpage{34}
   487   \item rewrite rules, \bold{27}
   495   \item rewrite rules, \bold{27}
   488     \subitem permutative, \bold{176}
   496     \subitem permutative, \bold{176}
   489   \item rewriting, \bold{27}
   497   \item rewriting, \bold{27}
   490   \item \isa {rotate_tac} (method), 30
   498   \item \isa {rotate_tac} (method), \hyperpage{30}
   491   \item \isa {rtrancl_refl} (theorem), \bold{112}
   499   \item \isa {rtrancl_refl} (theorem), \bold{112}
   492   \item \isa {rtrancl_trans} (theorem), \bold{112}
   500   \item \isa {rtrancl_trans} (theorem), \bold{112}
   493   \item rule induction, 128--130
   501   \item rule induction, 128--130
   494   \item rule inversion, 130--131, 139--140
   502   \item rule inversion, 130--131, 139--140
   495   \item \isa {rule_format} (attribute), 187
   503   \item \isa {rule_format} (attribute), \hyperpage{187}
   496   \item \isa {rule_tac} (method), 76
   504   \item \isa {rule_tac} (method), \hyperpage{76}
   497     \subitem and renaming, 83
   505     \subitem and renaming, \hyperpage{83}
   498 
   506 
   499   \indexspace
   507   \indexspace
   500 
   508 
   501   \item \isa {safe} (method), 91, 92
   509   \item \isa {safe} (method), \hyperpage{91, 92}
   502   \item safe rules, \bold{90}
   510   \item safe rules, \bold{90}
   503   \item \isacommand {sect} (command), 59
   511   \item \isacommand {sect} (command), \hyperpage{59}
   504   \item \isacommand {section} (command), 59
   512   \item \isacommand {section} (command), \hyperpage{59}
   505   \item selector
   513   \item selector
   506     \subitem record, 159
   514     \subitem record, \hyperpage{159}
   507   \item session, \bold{58}
   515   \item session, \bold{58}
   508   \item \isa {set} (type), 5, 105
   516   \item \isa {set} (type), \hyperpage{5}, \hyperpage{105}
   509   \item set comprehensions, 107--108
   517   \item set comprehensions, 107--108
   510   \item \isa {set_ext} (theorem), \bold{106}
   518   \item \isa {set_ext} (theorem), \bold{106}
   511   \item sets, 105--109
   519   \item sets, 105--109
   512     \subitem finite, 109
   520     \subitem finite, \hyperpage{109}
   513     \subitem notation for finite, \bold{107}
   521     \subitem notation for finite, \bold{107}
   514   \item settings, \see{flags}{1}
   522   \item settings, \see{flags}{1}
   515   \item \isa {show_brackets} (flag), 6
   523   \item \isa {show_brackets} (flag), \hyperpage{6}
   516   \item \isa {show_types} (flag), 5, 16
   524   \item \isa {show_types} (flag), \hyperpage{5}, \hyperpage{16}
   517   \item \isa {simp} (attribute), 11, 28
   525   \item \isa {simp} (attribute), \hyperpage{11}, \hyperpage{28}
   518   \item \isa {simp} (method), \bold{28}
   526   \item \isa {simp} (method), \bold{28}
   519   \item \isa {simp} del (attribute), 28
   527   \item \isa {simp} del (attribute), \hyperpage{28}
   520   \item \isa {simp_all} (method), 29, 38
   528   \item \isa {simp_all} (method), \hyperpage{29}, \hyperpage{38}
   521   \item simplification, 27--33, 175--178
   529   \item simplification, 27--33, 175--178
   522     \subitem of \isa{let}-expressions, 31
   530     \subitem of \isa{let}-expressions, \hyperpage{31}
   523     \subitem with definitions, 30
   531     \subitem with definitions, \hyperpage{30}
   524     \subitem with/of assumptions, 29
   532     \subitem with/of assumptions, \hyperpage{29}
   525   \item simplification rule, 177--178
   533   \item simplification rule, 177--178
   526   \item simplification rules, 28
   534   \item simplification rules, \hyperpage{28}
   527     \subitem adding and deleting, 29
   535     \subitem adding and deleting, \hyperpage{29}
   528   \item \isa {simplified} (attribute), 93, 96
   536   \item \isa {simplified} (attribute), \hyperpage{93}, \hyperpage{96}
   529   \item \isa {size} (constant), 17
   537   \item \isa {size} (constant), \hyperpage{17}
   530   \item \isa {snd} (constant), 24
   538   \item \isa {snd} (constant), \hyperpage{24}
   531   \item \isa {SOME} (symbol), 86
   539   \item \isa {SOME} (symbol), \hyperpage{86}
   532   \item \texttt {SOME}, \bold{209}
   540   \item \texttt {SOME}, \bold{209}
   533   \item \isa {Some} (constant), \bold{24}
   541   \item \isa {Some} (constant), \bold{24}
   534   \item \isa {some_equality} (theorem), \bold{86}
   542   \item \isa {some_equality} (theorem), \bold{86}
   535   \item \isa {someI} (theorem), \bold{86}
   543   \item \isa {someI} (theorem), \bold{86}
   536   \item \isa {someI2} (theorem), \bold{86}
   544   \item \isa {someI2} (theorem), \bold{86}
   537   \item \isa {someI_ex} (theorem), \bold{87}
   545   \item \isa {someI_ex} (theorem), \bold{87}
   538   \item sorts, 170
   546   \item sorts, \hyperpage{170}
   539   \item source comments, \bold{60}
   547   \item source comments, \bold{60}
   540   \item \isa {spec} (theorem), \bold{80}
   548   \item \isa {spec} (theorem), \bold{80}
   541   \item \isa {split} (attribute), 32
   549   \item \isa {split} (attribute), \hyperpage{32}
   542   \item \isa {split} (constant), 156
   550   \item \isa {split} (constant), \hyperpage{156}
   543   \item \isa {split} (method), 31, 156
   551   \item \isa {split} (method), \hyperpage{31}, \hyperpage{156}
   544   \item \isa {split} (modifier), 32
   552   \item \isa {split} (modifier), \hyperpage{32}
   545   \item split rule, \bold{32}
   553   \item split rule, \bold{32}
   546   \item \isa {split_if} (theorem), 32
   554   \item \isa {split_if} (theorem), \hyperpage{32}
   547   \item \isa {split_if_asm} (theorem), 32
   555   \item \isa {split_if_asm} (theorem), \hyperpage{32}
   548   \item \isa {ssubst} (theorem), \bold{77}
   556   \item \isa {ssubst} (theorem), \bold{77}
   549   \item structural induction, \see{induction, structural}{1}
   557   \item structural induction, \see{induction, structural}{1}
   550   \item subclasses, 164, 169
   558   \item subclasses, \hyperpage{164}, \hyperpage{169}
   551   \item subgoal numbering, 46
   559   \item subgoal numbering, \hyperpage{46}
   552   \item \isa {subgoal_tac} (method), 98
   560   \item \isa {subgoal_tac} (method), \hyperpage{98}
   553   \item subgoals, 12
   561   \item subgoals, \hyperpage{12}
   554   \item \isacommand {subsect} (command), 59
   562   \item \isacommand {subsect} (command), \hyperpage{59}
   555   \item \isacommand {subsection} (command), 59
   563   \item \isacommand {subsection} (command), \hyperpage{59}
   556   \item subset relation, \bold{106}
   564   \item subset relation, \bold{106}
   557   \item \isa {subsetD} (theorem), \bold{106}
   565   \item \isa {subsetD} (theorem), \bold{106}
   558   \item \isa {subsetI} (theorem), \bold{106}
   566   \item \isa {subsetI} (theorem), \bold{106}
   559   \item \isa {subst} (method), 77
   567   \item \isa {subst} (method), \hyperpage{77}
   560   \item substitution, 77--79
   568   \item substitution, 77--79
   561   \item \isacommand {subsubsect} (command), 59
   569   \item \isacommand {subsubsect} (command), \hyperpage{59}
   562   \item \isacommand {subsubsection} (command), 59
   570   \item \isacommand {subsubsection} (command), \hyperpage{59}
   563   \item \isa {Suc} (constant), 22
   571   \item \isa {Suc} (constant), \hyperpage{22}
   564   \item \isa {surj_def} (theorem), \bold{110}
   572   \item \isa {surj_def} (theorem), \bold{110}
   565   \item surjections, 110
   573   \item surjections, \hyperpage{110}
   566   \item \isa {sym} (theorem), \bold{94}
   574   \item \isa {sym} (theorem), \bold{94}
   567   \item symbols, \bold{54}
   575   \item symbols, \bold{54}
   568   \item syntax, 6, 11
   576   \item syntax, \hyperpage{6}, \hyperpage{11}
   569   \item \isacommand {syntax} (command), 55
   577   \item \isacommand {syntax} (command), \hyperpage{55}
   570   \item syntax (command), 56
   578   \item syntax (command), \hyperpage{56}
   571   \item syntax translations, \bold{56}
   579   \item syntax translations, \bold{56}
   572 
   580 
   573   \indexspace
   581   \indexspace
   574 
   582 
   575   \item tacticals, 99
   583   \item tacticals, 99
   576   \item tactics, 12
   584   \item tactics, \hyperpage{12}
   577   \item \isacommand {term} (command), 16
   585   \item \isacommand {term} (command), \hyperpage{16}
   578   \item term rewriting, \bold{27}
   586   \item term rewriting, \bold{27}
   579   \item termination, \see{functions, total}{1}
   587   \item termination, \see{functions, total}{1}
   580   \item terms, 5
   588   \item terms, 5
   581   \item text, \bold{61}
   589   \item text, \bold{61}
   582   \item text blocks, \bold{61}
   590   \item text blocks, \bold{61}
   583   \item \isa {THE} (symbol), 85
   591   \item \isa {THE} (symbol), \hyperpage{85}
   584   \item \isa {the_equality} (theorem), \bold{85}
   592   \item \isa {the_equality} (theorem), \bold{85}
   585   \item \isa {THEN} (attribute), \bold{94}, 96, 102
   593   \item \isa {THEN} (attribute), \bold{94}, \hyperpage{96}, 
   586   \item \isacommand {theorem} (command), \bold{11}, 13
   594 		\hyperpage{102}
       
   595   \item \isacommand {theorem} (command), \bold{11}, \hyperpage{13}
   587   \item theories, 4
   596   \item theories, 4
   588     \subitem abandoning, \bold{16}
   597     \subitem abandoning, \bold{16}
   589   \item \isacommand {theory} (command), 16
   598   \item \isacommand {theory} (command), \hyperpage{16}
   590   \item theory files, 4
   599   \item theory files, \hyperpage{4}
   591   \item \isacommand {thm} (command), 16
   600   \item \isacommand {thm} (command), \hyperpage{16}
   592   \item \isa {tl} (constant), 17
   601   \item \isa {tl} (constant), \hyperpage{17}
   593   \item \isa {ToyList} example, 9--14
   602   \item \isa {ToyList} example, 9--14
   594   \item \isa {trace_simp} (flag), 33
   603   \item \isa {trace_simp} (flag), \hyperpage{33}
   595   \item tracing the simplifier, \bold{33}
   604   \item tracing the simplifier, \bold{33}
   596   \item \isa {trancl_trans} (theorem), \bold{113}
   605   \item \isa {trancl_trans} (theorem), \bold{113}
   597   \item transition systems, 117
   606   \item transition systems, \hyperpage{117}
   598   \item \isacommand {translations} (command), 56
   607   \item \isacommand {translations} (command), \hyperpage{56}
   599   \item tries, 44--46
   608   \item tries, 44--46
   600   \item \isa {True} (constant), 5
   609   \item \isa {True} (constant), \hyperpage{5}
   601   \item \isa {truncate} (constant), 163
   610   \item \isa {truncate} (constant), \hyperpage{163}
   602   \item tuples, \see{pairs and tuples}{1}
   611   \item tuples, \see{pairs and tuples}{1}
   603   \item txt, \bold{61}
   612   \item txt, \bold{61}
   604   \item \isacommand {typ} (command), 16
   613   \item \isacommand {typ} (command), \hyperpage{16}
   605   \item type constraints, \bold{6}
   614   \item type constraints, \bold{6}
   606   \item type constructors, 5
   615   \item type constructors, \hyperpage{5}
   607   \item type inference, \bold{5}
   616   \item type inference, \bold{5}
   608   \item type synonyms, 25
   617   \item type synonyms, \hyperpage{25}
   609   \item type variables, 5
   618   \item type variables, \hyperpage{5}
   610   \item \isacommand {typedecl} (command), 117, 171
   619   \item \isacommand {typedecl} (command), \hyperpage{117}, 
       
   620 		\hyperpage{171}
   611   \item \isacommand {typedef} (command), 171--174
   621   \item \isacommand {typedef} (command), 171--174
   612   \item types, 4--5
   622   \item types, 4--5
   613     \subitem declaring, 171
   623     \subitem declaring, 171
   614     \subitem defining, 171--174
   624     \subitem defining, 171--174
   615   \item \isacommand {types} (command), 25
   625   \item \isacommand {types} (command), \hyperpage{25}
   616 
   626 
   617   \indexspace
   627   \indexspace
   618 
   628 
   619   \item Ullman, J. D., 145
   629   \item Ullman, J. D., \hyperpage{145}
   620   \item \texttt {UN}, \bold{209}
   630   \item \texttt {UN}, \bold{209}
   621   \item \texttt {Un}, \bold{209}
   631   \item \texttt {Un}, \bold{209}
   622   \item \isa {UN_E} (theorem), \bold{108}
   632   \item \isa {UN_E} (theorem), \bold{108}
   623   \item \isa {UN_I} (theorem), \bold{108}
   633   \item \isa {UN_I} (theorem), \bold{108}
   624   \item \isa {UN_iff} (theorem), \bold{108}
   634   \item \isa {UN_iff} (theorem), \bold{108}
   625   \item \isa {Un_subset_iff} (theorem), \bold{106}
   635   \item \isa {Un_subset_iff} (theorem), \bold{106}
   626   \item \isacommand {undo} (command), 16
   636   \item \isacommand {undo} (command), \hyperpage{16}
   627   \item \isa {unfold} (method), \bold{31}
   637   \item \isa {unfold} (method), \bold{31}
   628   \item unification, 76--79
   638   \item unification, 76--79
   629   \item \isa {UNION} (constant), 109
   639   \item \isa {UNION} (constant), \hyperpage{109}
   630   \item \texttt {Union}, \bold{209}
   640   \item \texttt {Union}, \bold{209}
   631   \item union
   641   \item union
   632     \subitem indexed, 108
   642     \subitem indexed, \hyperpage{108}
   633   \item \isa {Union_iff} (theorem), \bold{108}
   643   \item \isa {Union_iff} (theorem), \bold{108}
   634   \item \isa {unit} (type), 24
   644   \item \isa {unit} (type), \hyperpage{24}
   635   \item unknowns, 7, \bold{68}
   645   \item unknowns, \hyperpage{7}, \bold{68}
   636   \item unsafe rules, \bold{90}
   646   \item unsafe rules, \bold{90}
   637   \item update
   647   \item update
   638     \subitem record, 159
   648     \subitem record, \hyperpage{159}
   639   \item updating a function, \bold{109}
   649   \item updating a function, \bold{109}
   640 
   650 
   641   \indexspace
   651   \indexspace
   642 
   652 
   643   \item variables, 7
   653   \item variables, 7
   644     \subitem schematic, 7
   654     \subitem schematic, \hyperpage{7}
   645     \subitem type, 5
   655     \subitem type, \hyperpage{5}
   646   \item \isa {vimage_def} (theorem), \bold{111}
   656   \item \isa {vimage_def} (theorem), \bold{111}
   647 
   657 
   648   \indexspace
   658   \indexspace
   649 
   659 
   650   \item \isa {wf_induct} (theorem), \bold{115}
   660   \item \isa {wf_induct} (theorem), \bold{115}
   651   \item \isa {wf_inv_image} (theorem), \bold{115}
   661   \item \isa {wf_inv_image} (theorem), \bold{115}
   652   \item \isa {wf_less_than} (theorem), \bold{114}
   662   \item \isa {wf_less_than} (theorem), \bold{114}
   653   \item \isa {wf_lex_prod} (theorem), \bold{115}
   663   \item \isa {wf_lex_prod} (theorem), \bold{115}
   654   \item \isa {wf_measure} (theorem), \bold{115}
   664   \item \isa {wf_measure} (theorem), \bold{115}
   655   \item \isa {wf_subset} (theorem), 180
   665   \item \isa {wf_subset} (theorem), \hyperpage{180}
   656   \item \isa {while} (constant), 185
   666   \item \isa {while} (constant), \hyperpage{185}
   657   \item \isa {While_Combinator} (theory), 185
   667   \item \isa {While_Combinator} (theory), \hyperpage{185}
   658   \item \isa {while_rule} (theorem), 185
   668   \item \isa {while_rule} (theorem), \hyperpage{185}
   659 
   669 
   660   \indexspace
   670   \indexspace
   661 
   671 
   662   \item \isa {zadd_ac} (theorems), 153
   672   \item \isa {zadd_ac} (theorems), \hyperpage{153}
   663   \item \isa {zmult_ac} (theorems), 153
   673   \item \isa {zmult_ac} (theorems), \hyperpage{153}
   664 
   674 
   665 \end{theindex}
   675 \end{theindex}