doc-src/TutorialI/tutorial.ind
changeset 11647 0538cb0f7999
parent 11582 f666c1e4133d
child 11866 fbd097aec213
equal deleted inserted replaced
11646:6a7d80a139c6 11647:0538cb0f7999
     1 \begin{theindex}
     1 \begin{theindex}
     2 
     2 
     3   \item \ttall, \bold{187}
     3   \item \ttall, \bold{195}
     4   \item \texttt{?}, \bold{187}
     4   \item \texttt{?}, \bold{195}
     5   \item \isasymuniqex, \bold{187}
     5   \item \isasymuniqex, \bold{195}
     6   \item \ttuniquex, \bold{187}
     6   \item \ttuniquex, \bold{195}
     7   \item {\texttt {\&}}, \bold{187}
     7   \item {\texttt {\&}}, \bold{195}
     8   \item \verb$~$, \bold{187}
     8   \item \verb$~$, \bold{195}
     9   \item \verb$~=$, \bold{187}
     9   \item \verb$~=$, \bold{195}
    10   \item \ttor, \bold{187}
    10   \item \ttor, \bold{195}
    11   \item \texttt{[]}, \bold{7}
    11   \item \texttt{[]}, \bold{9}
    12   \item \texttt{\#}, \bold{7}
    12   \item \texttt{\#}, \bold{9}
    13   \item \texttt{\at}, \bold{8}, 187
    13   \item \texttt{\at}, \bold{10}, 195
    14   \item \isasymnotin, \bold{187}
    14   \item \isasymnotin, \bold{195}
    15   \item \verb$~:$, \bold{187}
    15   \item \verb$~:$, \bold{195}
    16   \item \isasymInter, \bold{187}
    16   \item \isasymInter, \bold{195}
    17   \item \isasymUnion, \bold{187}
    17   \item \isasymUnion, \bold{195}
    18   \item \isasyminverse, \bold{187}
    18   \item \isasyminverse, \bold{195}
    19   \item \verb$^-1$, \bold{187}
    19   \item \verb$^-1$, \bold{195}
    20   \item \isactrlsup{\isacharasterisk}, \bold{187}
    20   \item \isactrlsup{\isacharasterisk}, \bold{195}
    21   \item \verb$^$\texttt{*}, \bold{187}
    21   \item \verb$^$\texttt{*}, \bold{195}
    22   \item \isasymAnd, \bold{10}, \bold{187}
    22   \item \isasymAnd, \bold{12}, \bold{195}
    23   \item \ttAnd, \bold{187}
    23   \item \ttAnd, \bold{195}
    24   \item \isasymrightleftharpoons, 24
    24   \item \isasymrightleftharpoons, 26
    25   \item \isasymrightharpoonup, 24
    25   \item \isasymrightharpoonup, 26
    26   \item \isasymleftharpoondown, 24
    26   \item \isasymleftharpoondown, 26
    27   \item \emph {$\Rightarrow $}, \bold{3}
    27   \item \emph {$\Rightarrow $}, \bold{5}
    28   \item \ttlbr, \bold{187}
    28   \item \ttlbr, \bold{195}
    29   \item \ttrbr, \bold{187}
    29   \item \ttrbr, \bold{195}
    30   \item \texttt {\%}, \bold{187}
    30   \item \texttt {\%}, \bold{195}
    31   \item \texttt {;}, \bold{5}
    31   \item \texttt {;}, \bold{7}
    32   \item \isa {()} (constant), 22
    32   \item \isa {()} (constant), 24
    33   \item \isa {+} (tactical), 83
    33   \item \isa {+} (tactical), 89
    34   \item \isa {<*lex*>}, \see{lexicographic product}{1}
    34   \item \isa {<*lex*>}, \see{lexicographic product}{1}
    35   \item \isa {?} (tactical), 83
    35   \item \isa {?} (tactical), 89
    36   \item \texttt{|} (tactical), 83
    36   \item \texttt{|} (tactical), 89
    37 
    37 
    38   \indexspace
    38   \indexspace
    39 
    39 
    40   \item \isa {0} (constant), 20, 21, 133
    40   \item \isa {0} (constant), 22, 23, 141
    41   \item \isa {1} (symbol), 133
    41   \item \isa {1} (symbol), 141
    42   \item \isa {2} (symbol), 133
    42   \item \isa {2} (symbol), 141
    43 
    43 
    44   \indexspace
    44   \indexspace
    45 
    45 
    46   \item abandoning a proof, \bold{11}
    46   \item abandoning a proof, \bold{13}
    47   \item abandoning a theory, \bold{14}
    47   \item abandoning a theory, \bold{16}
    48   \item \isa {abs} (constant), 135
    48   \item \isa {abs} (constant), 143
    49   \item \texttt {abs}, \bold{187}
    49   \item \texttt {abs}, \bold{195}
    50   \item absolute value, 135
    50   \item absolute value, 143
    51   \item \isa {add} (modifier), 27
    51   \item \isa {add} (modifier), 29
    52   \item \isa {add_ac} (theorems), 134
    52   \item \isa {add_ac} (theorems), 142
    53   \item \isa {add_assoc} (theorem), \bold{134}
    53   \item \isa {add_assoc} (theorem), \bold{142}
    54   \item \isa {add_commute} (theorem), \bold{134}
    54   \item \isa {add_commute} (theorem), \bold{142}
    55   \item \isa {add_mult_distrib} (theorem), \bold{133}
    55   \item \isa {add_mult_distrib} (theorem), \bold{141}
    56   \item \texttt {ALL}, \bold{187}
    56   \item \texttt {ALL}, \bold{195}
    57   \item \isa {All} (constant), 93
    57   \item \isa {All} (constant), 99
    58   \item \isa {allE} (theorem), \bold{65}
    58   \item \isa {allE} (theorem), \bold{71}
    59   \item \isa {allI} (theorem), \bold{64}
    59   \item \isa {allI} (theorem), \bold{70}
    60   \item append function, 8--12
    60   \item append function, 10--14
    61   \item \isacommand {apply} (command), 13
    61   \item \isacommand {apply} (command), 15
    62   \item \isa {arg_cong} (theorem), \bold{80}
    62   \item \isa {arg_cong} (theorem), \bold{86}
    63   \item \isa {arith} (method), 21, 131
    63   \item \isa {arith} (method), 23, 139
    64   \item arithmetic operations
    64   \item arithmetic operations
    65     \subitem for \protect\isa{nat}, 21
    65     \subitem for \protect\isa{nat}, 23
    66   \item \textsc {ascii} symbols, \bold{187}
    66   \item \textsc {ascii} symbols, \bold{195}
    67   \item associative-commutative function, 156
    67   \item associative-commutative function, 164
    68   \item \isa {assumption} (method), 53
    68   \item \isa {assumption} (method), 59
    69   \item assumptions
    69   \item assumptions
    70     \subitem of subgoal, 10
    70     \subitem of subgoal, 12
    71     \subitem renaming, 66--67
    71     \subitem renaming, 72--73
    72     \subitem reusing, 67
    72     \subitem reusing, 73
    73   \item \isa {auto} (method), 35, 76
    73   \item \isa {auto} (method), 37, 82
    74   \item \isa {axclass}, 144--150
    74   \item \isa {axclass}, 152--158
    75   \item axiom of choice, 70
    75   \item axiom of choice, 76
    76   \item axiomatic type classes, 144--150
    76   \item axiomatic type classes, 152--158
    77 
    77 
    78   \indexspace
    78   \indexspace
    79 
    79 
    80   \item \isacommand {back} (command), 62
    80   \item \isacommand {back} (command), 68
    81   \item \isa {Ball} (constant), 93
    81   \item \isa {Ball} (constant), 99
    82   \item \isa {ballI} (theorem), \bold{92}
    82   \item \isa {ballI} (theorem), \bold{98}
    83   \item \isa {best} (method), 76
    83   \item \isa {best} (method), 82
    84   \item \isa {Bex} (constant), 93
    84   \item \isa {Bex} (constant), 99
    85   \item \isa {bexE} (theorem), \bold{92}
    85   \item \isa {bexE} (theorem), \bold{98}
    86   \item \isa {bexI} (theorem), \bold{92}
    86   \item \isa {bexI} (theorem), \bold{98}
    87   \item \isa {bij_def} (theorem), \bold{94}
    87   \item \isa {bij_def} (theorem), \bold{100}
    88   \item bijections, 94
    88   \item bijections, 100
    89   \item binary trees, 16
    89   \item binary trees, 18
    90   \item binomial coefficients, 93
    90   \item binomial coefficients, 99
    91   \item bisimulations, 100
    91   \item bisimulations, 106
    92   \item \isa {blast} (method), 73--74, 76
    92   \item \isa {blast} (method), 79--80, 82
    93   \item \isa {bool} (type), 2, 3
    93   \item \isa {bool} (type), 4, 5
    94   \item boolean expressions example, 18--20
    94   \item boolean expressions example, 20--22
    95   \item \isa {bspec} (theorem), \bold{92}
    95   \item \isa {bspec} (theorem), \bold{98}
    96   \item \isacommand{by} (command), 57
    96   \item \isacommand{by} (command), 63
    97 
    97 
    98   \indexspace
    98   \indexspace
    99 
    99 
   100   \item \isa {card} (constant), 93
   100   \item \isa {card} (constant), 99
   101   \item \isa {card_Pow} (theorem), \bold{93}
   101   \item \isa {card_Pow} (theorem), \bold{99}
   102   \item \isa {card_Un_Int} (theorem), \bold{93}
   102   \item \isa {card_Un_Int} (theorem), \bold{99}
   103   \item cardinality, 93
   103   \item cardinality, 99
   104   \item \isa {case} (symbol), 30, 31
   104   \item \isa {case} (symbol), 32, 33
   105   \item \isa {case} expressions, 3, 4, 16
   105   \item \isa {case} expressions, 5, 6, 18
   106   \item case distinctions, 17
   106   \item case distinctions, 19
   107   \item case splits, \bold{29}
   107   \item case splits, \bold{31}
   108   \item \isa {case_tac} (method), 17, 85, 139
   108   \item \isa {case_tac} (method), 19, 91, 147
   109   \item \isa {clarify} (method), 75, 76
   109   \item \isa {clarify} (method), 81, 82
   110   \item \isa {clarsimp} (method), 75, 76
   110   \item \isa {clarsimp} (method), 81, 82
   111   \item \isa {classical} (theorem), \bold{57}
   111   \item \isa {classical} (theorem), \bold{63}
   112   \item coinduction, \bold{100}
   112   \item coinduction, \bold{106}
   113   \item \isa {Collect} (constant), 93
   113   \item \isa {Collect} (constant), 99
   114   \item \isa {comp_def} (theorem), \bold{96}
   114   \item \isa {comp_def} (theorem), \bold{102}
   115   \item compiling expressions example, 34--36
   115   \item compiling expressions example, 36--38
   116   \item \isa {Compl_iff} (theorem), \bold{90}
   116   \item \isa {Compl_iff} (theorem), \bold{96}
   117   \item complement
   117   \item complement
   118     \subitem of a set, 89
   118     \subitem of a set, 95
   119   \item composition
   119   \item composition
   120     \subitem of functions, \bold{94}
   120     \subitem of functions, \bold{100}
   121     \subitem of relations, \bold{96}
   121     \subitem of relations, \bold{102}
   122   \item conclusion
   122   \item conclusion
   123     \subitem of subgoal, 10
   123     \subitem of subgoal, 12
   124   \item conditional expressions, \see{\isa{if} expressions}{1}
   124   \item conditional expressions, \see{\isa{if} expressions}{1}
   125   \item conditional simplification rules, 29
   125   \item conditional simplification rules, 31
   126   \item \isa {cong} (attribute), 156
   126   \item \isa {cong} (attribute), 164
   127   \item congruence rules, \bold{155}
   127   \item congruence rules, \bold{163}
   128   \item \isa {conjE} (theorem), \bold{55}
   128   \item \isa {conjE} (theorem), \bold{61}
   129   \item \isa {conjI} (theorem), \bold{52}
   129   \item \isa {conjI} (theorem), \bold{58}
   130   \item \isa {Cons} (constant), 7
   130   \item \isa {Cons} (constant), 9
   131   \item \isacommand {constdefs} (command), 23
   131   \item \isacommand {constdefs} (command), 25
   132   \item \isacommand {consts} (command), 8
   132   \item \isacommand {consts} (command), 10
   133   \item contrapositives, 57
   133   \item contrapositives, 63
   134   \item converse
   134   \item converse
   135     \subitem of a relation, \bold{96}
   135     \subitem of a relation, \bold{102}
   136   \item \isa {converse_iff} (theorem), \bold{96}
   136   \item \isa {converse_iff} (theorem), \bold{102}
   137   \item CTL, 105--110, 171--173
   137   \item CTL, 111--116, 179--181
   138 
   138 
   139   \indexspace
   139   \indexspace
   140 
   140 
   141   \item \isacommand {datatype} (command), 7, 36--41
   141   \item \isacommand {datatype} (command), 9, 38--43
   142   \item datatypes, 15--20
   142   \item datatypes, 17--22
   143     \subitem and nested recursion, 38, 42
   143     \subitem and nested recursion, 40, 44
   144     \subitem mutually recursive, 36
   144     \subitem mutually recursive, 38
   145     \subitem nested, 160
   145     \subitem nested, 168
   146   \item \isacommand {defer} (command), 14, 84
   146   \item \isacommand {defer} (command), 16, 90
   147   \item Definitional Approach, 24
   147   \item Definitional Approach, 26
   148   \item definitions, \bold{23}
   148   \item definitions, \bold{25}
   149     \subitem unfolding, \bold{28}
   149     \subitem unfolding, \bold{30}
   150   \item \isacommand {defs} (command), 23
   150   \item \isacommand {defs} (command), 25
   151   \item \isa {del} (modifier), 27
   151   \item \isa {del} (modifier), 29
   152   \item description operators, 69--71
   152   \item description operators, 75--77
   153   \item descriptions
   153   \item descriptions
   154     \subitem definite, 69
   154     \subitem definite, 75
   155     \subitem indefinite, 70
   155     \subitem indefinite, 76
   156   \item \isa {dest} (attribute), 86
   156   \item \isa {dest} (attribute), 92
   157   \item destruction rules, 55
   157   \item destruction rules, 61
   158   \item \isa {diff_mult_distrib} (theorem), \bold{133}
   158   \item \isa {diff_mult_distrib} (theorem), \bold{141}
   159   \item difference
   159   \item difference
   160     \subitem of sets, \bold{90}
   160     \subitem of sets, \bold{96}
   161   \item \isa {disjCI} (theorem), \bold{58}
   161   \item \isa {disjCI} (theorem), \bold{64}
   162   \item \isa {disjE} (theorem), \bold{54}
   162   \item \isa {disjE} (theorem), \bold{60}
   163   \item \isa {div} (symbol), 21
   163   \item \isa {div} (symbol), 23
   164   \item divides relation, 68, 79, 85--88, 134
   164   \item divides relation, 74, 85, 91--94, 142
   165   \item division
   165   \item division
   166     \subitem by negative numbers, 135
   166     \subitem by negative numbers, 143
   167     \subitem by zero, 134
   167     \subitem by zero, 142
   168     \subitem for type \protect\isa{nat}, 133
   168     \subitem for type \protect\isa{nat}, 141
   169   \item domain
   169   \item domain
   170     \subitem of a relation, 96
   170     \subitem of a relation, 102
   171   \item \isa {Domain_iff} (theorem), \bold{96}
   171   \item \isa {Domain_iff} (theorem), \bold{102}
   172   \item \isacommand {done} (command), 11
   172   \item \isacommand {done} (command), 13
   173   \item \isa {drule_tac} (method), 60, 80
   173   \item \isa {drule_tac} (method), 66, 86
   174   \item \isa {dvd_add} (theorem), \bold{134}
   174   \item \isa {dvd_add} (theorem), \bold{142}
   175   \item \isa {dvd_anti_sym} (theorem), \bold{134}
   175   \item \isa {dvd_anti_sym} (theorem), \bold{142}
   176   \item \isa {dvd_def} (theorem), \bold{134}
   176   \item \isa {dvd_def} (theorem), \bold{142}
   177 
   177 
   178   \indexspace
   178   \indexspace
   179 
   179 
   180   \item \isa {elim!} (attribute), 115
   180   \item \isa {elim!} (attribute), 121
   181   \item elimination rules, 53--54
   181   \item elimination rules, 59--60
   182   \item \isacommand {end} (command), 12
   182   \item \isacommand {end} (command), 14
   183   \item \isa {Eps} (constant), 93
   183   \item \isa {Eps} (constant), 99
   184   \item equality, 3
   184   \item equality, 5
   185     \subitem of functions, \bold{93}
   185     \subitem of functions, \bold{99}
   186     \subitem of records, 143
   186     \subitem of records, 151
   187     \subitem of sets, \bold{90}
   187     \subitem of sets, \bold{96}
   188   \item \isa {equalityE} (theorem), \bold{90}
   188   \item \isa {equalityE} (theorem), \bold{96}
   189   \item \isa {equalityI} (theorem), \bold{90}
   189   \item \isa {equalityI} (theorem), \bold{96}
   190   \item \isa {erule} (method), 54
   190   \item \isa {erule} (method), 60
   191   \item \isa {erule_tac} (method), 60
   191   \item \isa {erule_tac} (method), 66
   192   \item Euclid's algorithm, 85--88
   192   \item Euclid's algorithm, 91--94
   193   \item even numbers
   193   \item even numbers
   194     \subitem defining inductively, 111--115
   194     \subitem defining inductively, 117--121
   195   \item \texttt {EX}, \bold{187}
   195   \item \texttt {EX}, \bold{195}
   196   \item \isa {Ex} (constant), 93
   196   \item \isa {Ex} (constant), 99
   197   \item \isa {exE} (theorem), \bold{66}
   197   \item \isa {exE} (theorem), \bold{72}
   198   \item \isa {exI} (theorem), \bold{66}
   198   \item \isa {exI} (theorem), \bold{72}
   199   \item \isa {ext} (theorem), \bold{93}
   199   \item \isa {ext} (theorem), \bold{99}
   200   \item extensionality
   200   \item extensionality
   201     \subitem for functions, \bold{93, 94}
   201     \subitem for functions, \bold{99, 100}
   202     \subitem for records, 143
   202     \subitem for records, 151
   203     \subitem for sets, \bold{90}
   203     \subitem for sets, \bold{96}
   204   \item \ttEXU, \bold{187}
   204   \item \ttEXU, \bold{195}
   205 
   205 
   206   \indexspace
   206   \indexspace
   207 
   207 
   208   \item \isa {False} (constant), 3
   208   \item \isa {False} (constant), 5
   209   \item \isa {fast} (method), 76, 108
   209   \item \isa {fast} (method), 82, 114
   210   \item Fibonacci function, 44
   210   \item Fibonacci function, 46
   211   \item \isa {finite} (symbol), 93
   211   \item \isa {finite} (symbol), 99
   212   \item \isa {Finites} (constant), 93
   212   \item \isa {Finites} (constant), 99
   213   \item fixed points, 100
   213   \item fixed points, 106
   214   \item flags, 3, 4, 31
   214   \item flags, 5, 6, 33
   215     \subitem setting and resetting, 3
   215     \subitem setting and resetting, 5
   216   \item \isa {force} (method), 75, 76
   216   \item \isa {force} (method), 81, 82
   217   \item formulae, 3
   217   \item formulae, 5
   218   \item forward proof, 76--82
   218   \item forward proof, 82--88
   219   \item \isa {frule} (method), 67
   219   \item \isa {frule} (method), 73
   220   \item \isa {frule_tac} (method), 60
   220   \item \isa {frule_tac} (method), 66
   221   \item \isa {fst} (constant), 22
   221   \item \isa {fst} (constant), 24
   222   \item function types, 3
   222   \item function types, 5
   223   \item functions, 93--95
   223   \item functions, 99--101
   224     \subitem partial, 162
   224     \subitem partial, 170
   225     \subitem total, 9, 44--50
   225     \subitem total, 11, 46--52
   226     \subitem underdefined, 163
   226     \subitem underdefined, 171
   227 
   227 
   228   \indexspace
   228   \indexspace
   229 
   229 
   230   \item \isa {gcd} (constant), 77--78, 85--88
   230   \item \isa {gcd} (constant), 83--84, 91--94
   231   \item generalizing for induction, 113
   231   \item generalizing for induction, 119
   232   \item generalizing induction formulae, 32
   232   \item generalizing induction formulae, 34
   233   \item Girard, Jean-Yves, \fnote{55}
   233   \item Girard, Jean-Yves, \fnote{61}
   234   \item Gordon, Mike, 1
   234   \item Gordon, Mike, 3
   235   \item grammars
   235   \item grammars
   236     \subitem defining inductively, 124--129
   236     \subitem defining inductively, 130--135
   237   \item ground terms example, 119--124
   237   \item ground terms example, 125--130
   238 
   238 
   239   \indexspace
   239   \indexspace
   240 
   240 
   241   \item \isa {hd} (constant), 15, 35
   241   \item \isa {hd} (constant), 17, 37
   242   \item Hilbert's $\varepsilon$-operator, 70
   242   \item Hilbert's $\varepsilon$-operator, 76
   243   \item HOLCF, 41
   243   \item HOLCF, 43
   244   \item Hopcroft, J. E., 129
   244   \item Hopcroft, J. E., 135
   245   \item \isa {hypreal} (type), 137
   245   \item \isa {hypreal} (type), 145
   246 
   246 
   247   \indexspace
   247   \indexspace
   248 
   248 
   249   \item \isa {Id_def} (theorem), \bold{96}
   249   \item \isa {Id_def} (theorem), \bold{102}
   250   \item \isa {id_def} (theorem), \bold{94}
   250   \item \isa {id_def} (theorem), \bold{100}
   251   \item identifiers, \bold{4}
   251   \item identifiers, \bold{6}
   252     \subitem qualified, \bold{2}
   252     \subitem qualified, \bold{4}
   253   \item identity function, \bold{94}
   253   \item identity function, \bold{100}
   254   \item identity relation, \bold{96}
   254   \item identity relation, \bold{102}
   255   \item \isa {if} expressions, 3, 4
   255   \item \isa {if} expressions, 5, 6
   256     \subitem simplification of, 31
   256     \subitem simplification of, 33
   257     \subitem splitting of, 29, 47
   257     \subitem splitting of, 31, 49
   258   \item if-and-only-if, 3
   258   \item if-and-only-if, 5
   259   \item \isa {iff} (attribute), 74, 86, 114
   259   \item \isa {iff} (attribute), 80, 92, 120
   260   \item \isa {iffD1} (theorem), \bold{78}
   260   \item \isa {iffD1} (theorem), \bold{84}
   261   \item \isa {iffD2} (theorem), \bold{78}
   261   \item \isa {iffD2} (theorem), \bold{84}
   262   \item image
   262   \item image
   263     \subitem under a function, \bold{95}
   263     \subitem under a function, \bold{101}
   264     \subitem under a relation, \bold{96}
   264     \subitem under a relation, \bold{102}
   265   \item \isa {image_def} (theorem), \bold{95}
   265   \item \isa {image_def} (theorem), \bold{101}
   266   \item \isa {Image_iff} (theorem), \bold{96}
   266   \item \isa {Image_iff} (theorem), \bold{102}
   267   \item \isa {impI} (theorem), \bold{56}
   267   \item \isa {impI} (theorem), \bold{62}
   268   \item implication, 56--57
   268   \item implication, 62--63
   269   \item \isa {ind_cases} (method), 115
   269   \item \isa {ind_cases} (method), 121
   270   \item \isa {induct_tac} (method), 10, 17, 50, 170
   270   \item \isa {induct_tac} (method), 12, 19, 52, 178
   271   \item induction, 166--173
   271   \item induction, 174--181
   272     \subitem complete, 168
   272     \subitem complete, 176
   273     \subitem deriving new schemas, 170
   273     \subitem deriving new schemas, 178
   274     \subitem on a term, 167
   274     \subitem on a term, 175
   275     \subitem recursion, 49--50
   275     \subitem recursion, 51--52
   276     \subitem structural, 17
   276     \subitem structural, 19
   277     \subitem well-founded, 99
   277     \subitem well-founded, 105
   278   \item induction heuristics, 31--33
   278   \item induction heuristics, 33--35
   279   \item \isacommand {inductive} (command), 111
   279   \item \isacommand {inductive} (command), 117
   280   \item inductive definition
   280   \item inductive definition
   281     \subitem simultaneous, 125
   281     \subitem simultaneous, 131
   282   \item inductive definitions, 111--129
   282   \item inductive definitions, 117--135
   283   \item \isacommand {inductive\_cases} (command), 115, 123
   283   \item \isacommand {inductive\_cases} (command), 121, 129
   284   \item infinitely branching trees, 40
   284   \item infinitely branching trees, 42
   285   \item \isacommand{infixr} (annotation), 8
   285   \item \isacommand{infixr} (annotation), 10
   286   \item \isa {inj_on_def} (theorem), \bold{94}
   286   \item \isa {inj_on_def} (theorem), \bold{100}
   287   \item injections, 94
   287   \item injections, 100
   288   \item \isa {insert} (constant), 91
   288   \item \isa {insert} (constant), 97
   289   \item \isa {insert} (method), 81--82
   289   \item \isa {insert} (method), 87--88
   290   \item instance, \bold{145}
   290   \item instance, \bold{153}
   291   \item \texttt {INT}, \bold{187}
   291   \item \texttt {INT}, \bold{195}
   292   \item \texttt {Int}, \bold{187}
   292   \item \texttt {Int}, \bold{195}
   293   \item \isa {int} (type), 135
   293   \item \isa {int} (type), 143
   294   \item \isa {INT_iff} (theorem), \bold{92}
   294   \item \isa {INT_iff} (theorem), \bold{98}
   295   \item \isa {IntD1} (theorem), \bold{89}
   295   \item \isa {IntD1} (theorem), \bold{95}
   296   \item \isa {IntD2} (theorem), \bold{89}
   296   \item \isa {IntD2} (theorem), \bold{95}
   297   \item integers, 135
   297   \item integers, 143
   298   \item \isa {INTER} (constant), 93
   298   \item \isa {INTER} (constant), 99
   299   \item \texttt {Inter}, \bold{187}
   299   \item \texttt {Inter}, \bold{195}
   300   \item \isa {Inter_iff} (theorem), \bold{92}
   300   \item \isa {Inter_iff} (theorem), \bold{98}
   301   \item intersection, 89
   301   \item intersection, 95
   302     \subitem indexed, 92
   302     \subitem indexed, 98
   303   \item \isa {IntI} (theorem), \bold{89}
   303   \item \isa {IntI} (theorem), \bold{95}
   304   \item \isa {intro} (method), 58
   304   \item \isa {intro} (method), 64
   305   \item \isa {intro!} (attribute), 112
   305   \item \isa {intro!} (attribute), 118
   306   \item \isa {intro_classes} (method), 145
   306   \item \isa {intro_classes} (method), 153
   307   \item introduction rules, 52--53
   307   \item introduction rules, 58--59
   308   \item \isa {inv} (constant), 70
   308   \item \isa {inv} (constant), 76
   309   \item \isa {inv_image_def} (theorem), \bold{99}
   309   \item \isa {inv_image_def} (theorem), \bold{105}
   310   \item inverse
   310   \item inverse
   311     \subitem of a function, \bold{94}
   311     \subitem of a function, \bold{100}
   312     \subitem of a relation, \bold{96}
   312     \subitem of a relation, \bold{102}
   313   \item inverse image
   313   \item inverse image
   314     \subitem of a function, 95
   314     \subitem of a function, 101
   315     \subitem of a relation, 98
   315     \subitem of a relation, 104
   316   \item \isa {itrev} (constant), 32
   316   \item \isa {itrev} (constant), 34
   317 
   317 
   318   \indexspace
   318   \indexspace
   319 
   319 
   320   \item \isacommand {kill} (command), 14
   320   \item \isacommand {kill} (command), 16
   321 
   321 
   322   \indexspace
   322   \indexspace
   323 
   323 
   324   \item $\lambda$ expressions, 3
   324   \item $\lambda$ expressions, 5
   325   \item LCF, 41
   325   \item LCF, 43
   326   \item \isa {LEAST} (symbol), 21, 69
   326   \item \isa {LEAST} (symbol), 23, 75
   327   \item least number operator, \see{\protect\isa{LEAST}}{69}
   327   \item least number operator, \see{\protect\isa{LEAST}}{75}
   328   \item \isacommand {lemma} (command), 11
   328   \item \isacommand {lemma} (command), 13
   329   \item \isacommand {lemmas} (command), 77, 86
   329   \item \isacommand {lemmas} (command), 83, 92
   330   \item \isa {length} (symbol), 16
   330   \item \isa {length} (symbol), 18
   331   \item \isa {length_induct}, \bold{170}
   331   \item \isa {length_induct}, \bold{178}
   332   \item \isa {less_than} (constant), 98
   332   \item \isa {less_than} (constant), 104
   333   \item \isa {less_than_iff} (theorem), \bold{98}
   333   \item \isa {less_than_iff} (theorem), \bold{104}
   334   \item \isa {let} expressions, 3, 4, 29
   334   \item \isa {let} expressions, 5, 6, 31
   335   \item \isa {Let_def} (theorem), 29
   335   \item \isa {Let_def} (theorem), 31
   336   \item \isa {lex_prod_def} (theorem), \bold{99}
   336   \item \isa {lex_prod_def} (theorem), \bold{105}
   337   \item lexicographic product, \bold{99}, 158
   337   \item lexicographic product, \bold{105}, 166
   338   \item {\texttt{lfp}}
   338   \item {\texttt{lfp}}
   339     \subitem applications of, \see{CTL}{100}
   339     \subitem applications of, \see{CTL}{106}
   340   \item linear arithmetic, 20--22, 131
   340   \item linear arithmetic, 22--24, 139
   341   \item \isa {List} (theory), 15
   341   \item \isa {List} (theory), 17
   342   \item \isa {list} (type), 2, 7, 15
   342   \item \isa {list} (type), 4, 9, 17
   343   \item \isa {list.split} (theorem), 30
   343   \item \isa {list.split} (theorem), 32
   344   \item \isa {lists_mono} (theorem), \bold{121}
   344   \item \isa {lists_mono} (theorem), \bold{127}
   345   \item Lowe, Gavin, 176--177
   345   \item Lowe, Gavin, 184--185
   346 
   346 
   347   \indexspace
   347   \indexspace
   348 
   348 
   349   \item \isa {Main} (theory), 2
   349   \item \isa {Main} (theory), 4
   350   \item major premise, \bold{59}
   350   \item major premise, \bold{65}
   351   \item \isa {max} (constant), 21, 22
   351   \item \isa {max} (constant), 23, 24
   352   \item measure functions, 45, 98
   352   \item measure functions, 47, 104
   353   \item \isa {measure_def} (theorem), \bold{99}
   353   \item \isa {measure_def} (theorem), \bold{105}
   354   \item meta-logic, \bold{64}
   354   \item meta-logic, \bold{70}
   355   \item methods, \bold{14}
   355   \item methods, \bold{16}
   356   \item \isa {min} (constant), 21, 22
   356   \item \isa {min} (constant), 23, 24
   357   \item \isa {mod} (symbol), 21
   357   \item \isa {mod} (symbol), 23
   358   \item \isa {mod_div_equality} (theorem), \bold{133}
   358   \item \isa {mod_div_equality} (theorem), \bold{141}
   359   \item \isa {mod_mult_distrib} (theorem), \bold{133}
   359   \item \isa {mod_mult_distrib} (theorem), \bold{141}
   360   \item model checking example, 100--110
   360   \item model checking example, 106--116
   361   \item \emph{modus ponens}, 51, 56
   361   \item \emph{modus ponens}, 57, 62
   362   \item \isa {mono_def} (theorem), \bold{100}
   362   \item \isa {mono_def} (theorem), \bold{106}
   363   \item monotone functions, \bold{100}, 123
   363   \item monotone functions, \bold{106}, 129
   364     \subitem and inductive definitions, 121--122
   364     \subitem and inductive definitions, 127--128
   365   \item \isa {more} (constant), 140, 141
   365   \item \isa {more} (constant), 148, 149
   366   \item \isa {mp} (theorem), \bold{56}
   366   \item \isa {mp} (theorem), \bold{62}
   367   \item \isa {mult_ac} (theorems), 134
   367   \item \isa {mult_ac} (theorems), 142
   368   \item multiple inheritance, \bold{149}
   368   \item multiple inheritance, \bold{157}
   369   \item multiset ordering, \bold{99}
   369   \item multiset ordering, \bold{105}
   370 
   370 
   371   \indexspace
   371   \indexspace
   372 
   372 
   373   \item \isa {nat} (type), 2, 20, 133--134
   373   \item \isa {nat} (type), 4, 22, 141--142
   374   \item \isa {nat_less_induct} (theorem), 168
   374   \item \isa {nat_less_induct} (theorem), 176
   375   \item natural deduction, 51--52
   375   \item natural deduction, 57--58
   376   \item natural numbers, 20, 133--134
   376   \item natural numbers, 22, 141--142
   377   \item Needham-Schroeder protocol, 175--177
   377   \item Needham-Schroeder protocol, 183--185
   378   \item negation, 57--59
   378   \item negation, 63--65
   379   \item \isa {Nil} (constant), 7
   379   \item \isa {Nil} (constant), 9
   380   \item \isa {no_asm} (modifier), 27
   380   \item \isa {no_asm} (modifier), 29
   381   \item \isa {no_asm_simp} (modifier), 27
   381   \item \isa {no_asm_simp} (modifier), 29
   382   \item \isa {no_asm_use} (modifier), 27
   382   \item \isa {no_asm_use} (modifier), 29
   383   \item non-standard reals, 137
   383   \item non-standard reals, 145
   384   \item \isa {None} (constant), \bold{22}
   384   \item \isa {None} (constant), \bold{24}
   385   \item \isa {notE} (theorem), \bold{57}
   385   \item \isa {notE} (theorem), \bold{63}
   386   \item \isa {notI} (theorem), \bold{57}
   386   \item \isa {notI} (theorem), \bold{63}
   387   \item numbers, 131--137
   387   \item numbers, 139--145
   388   \item numeric literals, 132
   388   \item numeric literals, 140
   389     \subitem for type \protect\isa{nat}, 133
   389     \subitem for type \protect\isa{nat}, 141
   390     \subitem for type \protect\isa{real}, 136
   390     \subitem for type \protect\isa{real}, 144
   391 
   391 
   392   \indexspace
   392   \indexspace
   393 
   393 
   394   \item \isa {O} (symbol), 96
   394   \item \isa {O} (symbol), 102
   395   \item \texttt {o}, \bold{187}
   395   \item \texttt {o}, \bold{195}
   396   \item \isa {o_def} (theorem), \bold{94}
   396   \item \isa {o_def} (theorem), \bold{100}
   397   \item \isa {OF} (attribute), 79--80
   397   \item \isa {OF} (attribute), 85--86
   398   \item \isa {of} (attribute), 77, 80
   398   \item \isa {of} (attribute), 83, 86
   399   \item \isa {only} (modifier), 27
   399   \item \isa {only} (modifier), 29
   400   \item \isacommand {oops} (command), 11
   400   \item \isacommand {oops} (command), 13
   401   \item \isa {option} (type), \bold{22}
   401   \item \isa {option} (type), \bold{24}
   402   \item ordered rewriting, \bold{156}
   402   \item ordered rewriting, \bold{164}
   403   \item overloading, 21, 144--146
   403   \item overloading, 23, 152--154
   404     \subitem and arithmetic, 132
   404     \subitem and arithmetic, 140
   405 
   405 
   406   \indexspace
   406   \indexspace
   407 
   407 
   408   \item pairs and tuples, 22, 137--140
   408   \item pairs and tuples, 24, 145--148
   409   \item parent theories, \bold{2}
   409   \item parent theories, \bold{4}
   410   \item pattern matching
   410   \item pattern matching
   411     \subitem and \isacommand{recdef}, 45
   411     \subitem and \isacommand{recdef}, 47
   412   \item patterns
   412   \item patterns
   413     \subitem higher-order, \bold{157}
   413     \subitem higher-order, \bold{165}
   414   \item PDL, 102--104
   414   \item PDL, 108--110
   415   \item \isacommand {pr} (command), 14, 84
   415   \item \isacommand {pr} (command), 16, 90
   416   \item \isacommand {prefer} (command), 14, 84
   416   \item \isacommand {prefer} (command), 16, 90
   417   \item primitive recursion, \see{recursion, primitive}{1}
   417   \item primitive recursion, \see{recursion, primitive}{1}
   418   \item \isacommand {primrec} (command), 8, 16, 36--41
   418   \item \isacommand {primrec} (command), 10, 18, 38--43
   419   \item product type, \see{pairs and tuples}{1}
   419   \item product type, \see{pairs and tuples}{1}
   420   \item Proof General, \bold{5}
   420   \item Proof General, \bold{7}
   421   \item proof state, 10
   421   \item proof state, 12
   422   \item proofs
   422   \item proofs
   423     \subitem abandoning, \bold{11}
   423     \subitem abandoning, \bold{13}
   424     \subitem examples of failing, 71--73
   424     \subitem examples of failing, 77--79
   425   \item protocols
   425   \item protocols
   426     \subitem security, 175--185
   426     \subitem security, 183--193
   427 
   427 
   428   \indexspace
   428   \indexspace
   429 
   429 
   430   \item quantifiers, 3
   430   \item quantifiers, 5
   431     \subitem and inductive definitions, 119--121
   431     \subitem and inductive definitions, 125--127
   432     \subitem existential, 66
   432     \subitem existential, 72
   433     \subitem for sets, 92
   433     \subitem for sets, 98
   434     \subitem instantiating, 68
   434     \subitem instantiating, 74
   435     \subitem universal, 63--66
   435     \subitem universal, 69--72
   436 
   436 
   437   \indexspace
   437   \indexspace
   438 
   438 
   439   \item \isa {r_into_rtrancl} (theorem), \bold{96}
   439   \item \isa {r_into_rtrancl} (theorem), \bold{102}
   440   \item \isa {r_into_trancl} (theorem), \bold{97}
   440   \item \isa {r_into_trancl} (theorem), \bold{103}
   441   \item range
   441   \item range
   442     \subitem of a function, 95
   442     \subitem of a function, 101
   443     \subitem of a relation, 96
   443     \subitem of a relation, 102
   444   \item \isa {range} (symbol), 95
   444   \item \isa {range} (symbol), 101
   445   \item \isa {Range_iff} (theorem), \bold{96}
   445   \item \isa {Range_iff} (theorem), \bold{102}
   446   \item \isa {Real} (theory), 137
   446   \item \isa {Real} (theory), 145
   447   \item \isa {real} (type), 136--137
   447   \item \isa {real} (type), 144--145
   448   \item real numbers, 136--137
   448   \item real numbers, 144--145
   449   \item \isacommand {recdef} (command), 44--50, 98, 158--166
   449   \item \isacommand {recdef} (command), 46--52, 104, 166--174
   450     \subitem and numeric literals, 132
   450     \subitem and numeric literals, 140
   451   \item \isa {recdef_cong} (attribute), 162
   451   \item \isa {recdef_cong} (attribute), 170
   452   \item \isa {recdef_simp} (attribute), 46
   452   \item \isa {recdef_simp} (attribute), 48
   453   \item \isa {recdef_wf} (attribute), 160
   453   \item \isa {recdef_wf} (attribute), 168
   454   \item \isacommand {record} (command), 140
   454   \item \isacommand {record} (command), 148
   455   \item \isa {record_split} (method), 143
   455   \item \isa {record_split} (method), 151
   456   \item records, 140--144
   456   \item records, 148--152
   457     \subitem extensible, 141--142
   457     \subitem extensible, 149--150
   458   \item recursion
   458   \item recursion
   459     \subitem guarded, 163
   459     \subitem guarded, 171
   460     \subitem primitive, 16
   460     \subitem primitive, 18
   461     \subitem well-founded, \bold{159}
   461     \subitem well-founded, \bold{167}
   462   \item recursion induction, 49--50
   462   \item recursion induction, 51--52
   463   \item \isacommand {redo} (command), 14
   463   \item \isacommand {redo} (command), 16
   464   \item reflexive and transitive closure, 96--98
   464   \item reflexive and transitive closure, 102--104
   465   \item reflexive transitive closure
   465   \item reflexive transitive closure
   466     \subitem defining inductively, 116--119
   466     \subitem defining inductively, 122--125
   467   \item relations, 95--98
   467   \item relations, 101--104
   468     \subitem well-founded, 98--99
   468     \subitem well-founded, 104--105
   469   \item \isa {rename_tac} (method), 66--67
   469   \item \isa {rename_tac} (method), 72--73
   470   \item \isa {rev} (constant), 8--12, 32
   470   \item \isa {rev} (constant), 10--14, 34
   471   \item rewrite rules, \bold{25}
   471   \item rewrite rules, \bold{27}
   472     \subitem permutative, \bold{156}
   472     \subitem permutative, \bold{164}
   473   \item rewriting, \bold{25}
   473   \item rewriting, \bold{27}
   474   \item \isa {rotate_tac} (method), 28
   474   \item \isa {rotate_tac} (method), 30
   475   \item \isa {rtrancl_refl} (theorem), \bold{96}
   475   \item \isa {rtrancl_refl} (theorem), \bold{102}
   476   \item \isa {rtrancl_trans} (theorem), \bold{96}
   476   \item \isa {rtrancl_trans} (theorem), \bold{102}
   477   \item rule induction, 112--114
   477   \item rule induction, 118--120
   478   \item rule inversion, 114--115, 123--124
   478   \item rule inversion, 120--121, 129--130
   479   \item \isa {rule_format} (attribute), 167
   479   \item \isa {rule_format} (attribute), 175
   480   \item \isa {rule_tac} (method), 60
   480   \item \isa {rule_tac} (method), 66
   481     \subitem and renaming, 67
   481     \subitem and renaming, 73
   482 
   482 
   483   \indexspace
   483   \indexspace
   484 
   484 
   485   \item \isa {safe} (method), 75, 76
   485   \item \isa {safe} (method), 81, 82
   486   \item safe rules, \bold{74}
   486   \item safe rules, \bold{80}
   487   \item \isa {set} (type), 2, 89
   487   \item \isa {set} (type), 4, 95
   488   \item set comprehensions, 91--92
   488   \item set comprehensions, 97--98
   489   \item \isa {set_ext} (theorem), \bold{90}
   489   \item \isa {set_ext} (theorem), \bold{96}
   490   \item sets, 89--93
   490   \item sets, 95--99
   491     \subitem finite, 93
   491     \subitem finite, 99
   492     \subitem notation for finite, \bold{91}
   492     \subitem notation for finite, \bold{97}
   493   \item settings, \see{flags}{1}
   493   \item settings, \see{flags}{1}
   494   \item \isa {show_brackets} (flag), 4
   494   \item \isa {show_brackets} (flag), 6
   495   \item \isa {show_types} (flag), 3, 14
   495   \item \isa {show_types} (flag), 5, 16
   496   \item \isa {simp} (attribute), 9, 26
   496   \item \isa {simp} (attribute), 11, 28
   497   \item \isa {simp} (method), \bold{26}
   497   \item \isa {simp} (method), \bold{28}
   498   \item \isa {simp} del (attribute), 26
   498   \item \isa {simp} del (attribute), 28
   499   \item \isa {simp_all} (method), 26, 35
   499   \item \isa {simp_all} (method), 28, 37
   500   \item simplification, 25--31, 155--158
   500   \item simplification, 27--33, 163--166
   501     \subitem of \isa{let}-expressions, 29
   501     \subitem of \isa{let}-expressions, 31
   502     \subitem with definitions, 28
   502     \subitem with definitions, 30
   503     \subitem with/of assumptions, 27
   503     \subitem with/of assumptions, 29
   504   \item simplification rule, 157--158
   504   \item simplification rule, 165--166
   505   \item simplification rules, 26
   505   \item simplification rules, 28
   506     \subitem adding and deleting, 27
   506     \subitem adding and deleting, 29
   507   \item \isa {simplified} (attribute), 77, 80
   507   \item \isa {simplified} (attribute), 83, 86
   508   \item \isa {size} (constant), 15
   508   \item \isa {size} (constant), 17
   509   \item \isa {snd} (constant), 22
   509   \item \isa {snd} (constant), 24
   510   \item \isa {SOME} (symbol), 70
   510   \item \isa {SOME} (symbol), 76
   511   \item \texttt {SOME}, \bold{187}
   511   \item \texttt {SOME}, \bold{195}
   512   \item \isa {Some} (constant), \bold{22}
   512   \item \isa {Some} (constant), \bold{24}
   513   \item \isa {some_equality} (theorem), \bold{70}
   513   \item \isa {some_equality} (theorem), \bold{76}
   514   \item \isa {someI} (theorem), \bold{70}
   514   \item \isa {someI} (theorem), \bold{76}
   515   \item \isa {someI2} (theorem), \bold{70}
   515   \item \isa {someI2} (theorem), \bold{76}
   516   \item \isa {someI_ex} (theorem), \bold{71}
   516   \item \isa {someI_ex} (theorem), \bold{77}
   517   \item sorts, 150
   517   \item sorts, 158
   518   \item \isa {spec} (theorem), \bold{64}
   518   \item \isa {spec} (theorem), \bold{70}
   519   \item \isa {split} (attribute), 30
   519   \item \isa {split} (attribute), 32
   520   \item \isa {split} (constant), 137
   520   \item \isa {split} (constant), 145
   521   \item \isa {split} (method), 29, 138
   521   \item \isa {split} (method), 31, 146
   522   \item \isa {split} (modifier), 30
   522   \item \isa {split} (modifier), 32
   523   \item split rule, \bold{30}
   523   \item split rule, \bold{32}
   524   \item \isa {split_if} (theorem), 30
   524   \item \isa {split_if} (theorem), 32
   525   \item \isa {split_if_asm} (theorem), 30
   525   \item \isa {split_if_asm} (theorem), 32
   526   \item \isa {ssubst} (theorem), \bold{61}
   526   \item \isa {ssubst} (theorem), \bold{67}
   527   \item structural induction, \see{induction, structural}{1}
   527   \item structural induction, \see{induction, structural}{1}
   528   \item subclasses, 144, 148
   528   \item subclasses, 152, 156
   529   \item subgoal numbering, 44
   529   \item subgoal numbering, 46
   530   \item \isa {subgoal_tac} (method), 82
   530   \item \isa {subgoal_tac} (method), 88
   531   \item subgoals, 10
   531   \item subgoals, 12
   532   \item subset relation, \bold{90}
   532   \item subset relation, \bold{96}
   533   \item \isa {subsetD} (theorem), \bold{90}
   533   \item \isa {subsetD} (theorem), \bold{96}
   534   \item \isa {subsetI} (theorem), \bold{90}
   534   \item \isa {subsetI} (theorem), \bold{96}
   535   \item \isa {subst} (method), 61
   535   \item \isa {subst} (method), 67
   536   \item substitution, 61--63
   536   \item substitution, 67--69
   537   \item \isa {Suc} (constant), 20
   537   \item \isa {Suc} (constant), 22
   538   \item \isa {surj_def} (theorem), \bold{94}
   538   \item \isa {surj_def} (theorem), \bold{100}
   539   \item surjections, 94
   539   \item surjections, 100
   540   \item \isa {sym} (theorem), \bold{78}
   540   \item \isa {sym} (theorem), \bold{84}
   541   \item syntax, 4, 9
   541   \item syntax, 6, 11
   542   \item syntax translations, 24
   542   \item syntax translations, 26
   543 
   543 
   544   \indexspace
   544   \indexspace
   545 
   545 
   546   \item tacticals, 83
   546   \item tacticals, 89
   547   \item tactics, 10
   547   \item tactics, 12
   548   \item \isacommand {term} (command), 14
   548   \item \isacommand {term} (command), 16
   549   \item term rewriting, \bold{25}
   549   \item term rewriting, \bold{27}
   550   \item termination, \see{functions, total}{1}
   550   \item termination, \see{functions, total}{1}
   551   \item terms, 3
   551   \item terms, 5
   552   \item \isa {THE} (symbol), 69
   552   \item \isa {THE} (symbol), 75
   553   \item \isa {the_equality} (theorem), \bold{69}
   553   \item \isa {the_equality} (theorem), \bold{75}
   554   \item \isa {THEN} (attribute), \bold{78}, 80, 86
   554   \item \isa {THEN} (attribute), \bold{84}, 86, 92
   555   \item \isacommand {theorem} (command), \bold{9}, 11
   555   \item \isacommand {theorem} (command), \bold{11}, 13
   556   \item theories, 2
   556   \item theories, 4
   557     \subitem abandoning, \bold{14}
   557     \subitem abandoning, \bold{16}
   558   \item \isacommand {theory} (command), 14
   558   \item \isacommand {theory} (command), 16
   559   \item theory files, 2
   559   \item theory files, 4
   560   \item \isacommand {thm} (command), 14
   560   \item \isacommand {thm} (command), 16
   561   \item \isa {tl} (constant), 15
   561   \item \isa {tl} (constant), 17
   562   \item \isa {ToyList} example, 7--13
   562   \item \isa {ToyList} example, 9--15
   563   \item \isa {trace_simp} (flag), 31
   563   \item \isa {trace_simp} (flag), 33
   564   \item tracing the simplifier, \bold{31}
   564   \item tracing the simplifier, \bold{33}
   565   \item \isa {trancl_trans} (theorem), \bold{97}
   565   \item \isa {trancl_trans} (theorem), \bold{103}
   566   \item transition systems, 101
   566   \item transition systems, 107
   567   \item \isacommand {translations} (command), 24
   567   \item \isacommand {translations} (command), 26
   568   \item tries, 41--44
   568   \item tries, 43--46
   569   \item \isa {True} (constant), 3
   569   \item \isa {True} (constant), 5
   570   \item tuples, \see{pairs and tuples}{1}
   570   \item tuples, \see{pairs and tuples}{1}
   571   \item \isacommand {typ} (command), 14
   571   \item \isacommand {typ} (command), 16
   572   \item type constraints, \bold{4}
   572   \item type constraints, \bold{6}
   573   \item type constructors, 2
   573   \item type constructors, 4
   574   \item type inference, \bold{3}
   574   \item type inference, \bold{5}
   575   \item type synonyms, 23
   575   \item type synonyms, 25
   576   \item type variables, 3
   576   \item type variables, 5
   577   \item \isacommand {typedecl} (command), 101, 150
   577   \item \isacommand {typedecl} (command), 107, 158
   578   \item \isacommand {typedef} (command), 151--154
   578   \item \isacommand {typedef} (command), 159--162
   579   \item types, 2--3
   579   \item types, 4--5
   580     \subitem declaring, 150--151
   580     \subitem declaring, 158--159
   581     \subitem defining, 151--154
   581     \subitem defining, 159--162
   582   \item \isacommand {types} (command), 23
   582   \item \isacommand {types} (command), 25
   583 
   583 
   584   \indexspace
   584   \indexspace
   585 
   585 
   586   \item Ullman, J. D., 129
   586   \item Ullman, J. D., 135
   587   \item \texttt {UN}, \bold{187}
   587   \item \texttt {UN}, \bold{195}
   588   \item \texttt {Un}, \bold{187}
   588   \item \texttt {Un}, \bold{195}
   589   \item \isa {UN_E} (theorem), \bold{92}
   589   \item \isa {UN_E} (theorem), \bold{98}
   590   \item \isa {UN_I} (theorem), \bold{92}
   590   \item \isa {UN_I} (theorem), \bold{98}
   591   \item \isa {UN_iff} (theorem), \bold{92}
   591   \item \isa {UN_iff} (theorem), \bold{98}
   592   \item \isa {Un_subset_iff} (theorem), \bold{90}
   592   \item \isa {Un_subset_iff} (theorem), \bold{96}
   593   \item \isacommand {undo} (command), 14
   593   \item \isacommand {undo} (command), 16
   594   \item unification, 60--63
   594   \item unification, 66--69
   595   \item \isa {UNION} (constant), 93
   595   \item \isa {UNION} (constant), 99
   596   \item \texttt {Union}, \bold{187}
   596   \item \texttt {Union}, \bold{195}
   597   \item union
   597   \item union
   598     \subitem indexed, 92
   598     \subitem indexed, 98
   599   \item \isa {Union_iff} (theorem), \bold{92}
   599   \item \isa {Union_iff} (theorem), \bold{98}
   600   \item \isa {unit} (type), 22
   600   \item \isa {unit} (type), 24
   601   \item unknowns, 4, \bold{52}
   601   \item unknowns, 6, \bold{58}
   602   \item unsafe rules, \bold{74}
   602   \item unsafe rules, \bold{80}
   603   \item updating a function, \bold{93}
   603   \item updating a function, \bold{99}
   604 
   604 
   605   \indexspace
   605   \indexspace
   606 
   606 
   607   \item variables, 4--5
   607   \item variables, 6--7
   608     \subitem schematic, 4
   608     \subitem schematic, 6
   609     \subitem type, 3
   609     \subitem type, 5
   610   \item \isa {vimage_def} (theorem), \bold{95}
   610   \item \isa {vimage_def} (theorem), \bold{101}
   611 
   611 
   612   \indexspace
   612   \indexspace
   613 
   613 
   614   \item Wenzel, Markus, vii
   614   \item Wenzel, Markus, vii
   615   \item \isa {wf_induct} (theorem), \bold{99}
   615   \item \isa {wf_induct} (theorem), \bold{105}
   616   \item \isa {wf_inv_image} (theorem), \bold{99}
   616   \item \isa {wf_inv_image} (theorem), \bold{105}
   617   \item \isa {wf_less_than} (theorem), \bold{98}
   617   \item \isa {wf_less_than} (theorem), \bold{104}
   618   \item \isa {wf_lex_prod} (theorem), \bold{99}
   618   \item \isa {wf_lex_prod} (theorem), \bold{105}
   619   \item \isa {wf_measure} (theorem), \bold{99}
   619   \item \isa {wf_measure} (theorem), \bold{105}
   620   \item \isa {wf_subset} (theorem), 160
   620   \item \isa {wf_subset} (theorem), 168
   621   \item \isa {while} (constant), 165
   621   \item \isa {while} (constant), 173
   622   \item \isa {While_Combinator} (theory), 165
   622   \item \isa {While_Combinator} (theory), 173
   623   \item \isa {while_rule} (theorem), 165
   623   \item \isa {while_rule} (theorem), 173
   624 
   624 
   625   \indexspace
   625   \indexspace
   626 
   626 
   627   \item \isa {zadd_ac} (theorems), 135
   627   \item \isa {zadd_ac} (theorems), 143
   628   \item \isa {zmult_ac} (theorems), 135
   628   \item \isa {zmult_ac} (theorems), 143
   629 
   629 
   630 \end{theindex}
   630 \end{theindex}