doc-src/Logics/logics.ind
changeset 6141 a6922171b396
parent 6098 8648c6651f07
child 6428 075f263a57bd
equal deleted inserted replaced
6140:af32e2c3f77a 6141:a6922171b396
     1 \begin{theindex}
     1 \begin{theindex}
     2 
     2 
     3   \item {\tt !} symbol, 2, 4, 11, 12, 24
     3   \item {\tt !} symbol, 6, 8, 15, 16, 28
     4   \item {\tt[]} symbol, 24
     4   \item {\tt[]} symbol, 28
     5   \item {\tt\#} symbol, 24
     5   \item {\tt\#} symbol, 28
     6   \item {\tt\#*} symbol, 80
     6   \item {\tt\#*} symbol, 83
     7   \item {\tt\#+} symbol, 80
     7   \item {\tt\#+} symbol, 83
     8   \item {\tt\&} symbol, 2, 56
     8   \item {\tt\&} symbol, 6, 59
     9   \item {\tt *} symbol, 3, 21, 71
     9   \item {\tt *} symbol, 7, 25, 74
    10   \item {\tt *} type, 19
    10   \item {\tt *} type, 23
    11   \item {\tt +} symbol, 3, 21, 71
    11   \item {\tt +} symbol, 7, 25, 74
    12   \item {\tt +} type, 19
    12   \item {\tt +} type, 23
    13   \item {\tt -} symbol, 3, 21, 80
    13   \item {\tt -} symbol, 7, 25, 83
    14   \item {\tt -->} symbol, 2, 56, 71
    14   \item {\tt -->} symbol, 6, 59, 74
    15   \item {\tt :} symbol, 10
    15   \item {\tt :} symbol, 14
    16   \item {\tt <} constant, 22
    16   \item {\tt <} constant, 26
    17   \item {\tt <} symbol, 21
    17   \item {\tt <} symbol, 25
    18   \item {\tt <->} symbol, 56
    18   \item {\tt <->} symbol, 59
    19   \item {\tt <=} constant, 22
    19   \item {\tt <=} constant, 26
    20   \item {\tt <=} symbol, 10
    20   \item {\tt <=} symbol, 14
    21   \item {\tt =} symbol, 2, 56, 71
    21   \item {\tt =} symbol, 6, 59, 74
    22   \item {\tt ?} symbol, 2, 4, 11, 12
    22   \item {\tt ?} symbol, 6, 8, 15, 16
    23   \item {\tt ?!} symbol, 2
    23   \item {\tt ?!} symbol, 6
    24   \item {\tt\at} symbol, 2, 24
    24   \item {\tt\at} symbol, 6, 28
    25   \item {\tt `} symbol, 71
    25   \item {\tt `} symbol, 74
    26   \item {\tt ``} symbol, 10
    26   \item {\tt ``} symbol, 14
    27   \item \verb'{}' symbol, 10
    27   \item \verb'{}' symbol, 14
    28   \item {\tt |} symbol, 2, 56
    28   \item {\tt |} symbol, 6, 59
    29   \item {\tt |-|} symbol, 80
    29   \item {\tt |-|} symbol, 83
    30 
    30 
    31   \indexspace
    31   \indexspace
    32 
    32 
    33   \item {\tt 0} constant, 21, 69
    33   \item {\tt 0} constant, 25, 72
    34 
    34 
    35   \indexspace
    35   \indexspace
    36 
    36 
    37   \item {\tt absdiff_def} theorem, 80
    37   \item {\tt absdiff_def} theorem, 83
    38   \item {\tt add_assoc} theorem, 80
    38   \item {\tt add_assoc} theorem, 83
    39   \item {\tt add_commute} theorem, 80
    39   \item {\tt add_commute} theorem, 83
    40   \item {\tt add_def} theorem, 80
    40   \item {\tt add_def} theorem, 83
    41   \item {\tt add_inverse_diff} theorem, 80
    41   \item {\tt add_inverse_diff} theorem, 83
    42   \item {\tt add_mp_tac}, \bold{78}
    42   \item {\tt add_mp_tac}, \bold{81}
    43   \item {\tt add_mult_dist} theorem, 80
    43   \item {\tt add_mult_dist} theorem, 83
    44   \item {\tt add_safes}, \bold{62}
    44   \item {\tt add_safes}, \bold{65}
    45   \item {\tt add_typing} theorem, 80
    45   \item {\tt add_typing} theorem, 83
    46   \item {\tt add_unsafes}, \bold{62}
    46   \item {\tt add_unsafes}, \bold{65}
    47   \item {\tt addC0} theorem, 80
    47   \item {\tt addC0} theorem, 83
    48   \item {\tt addC_succ} theorem, 80
    48   \item {\tt addC_succ} theorem, 83
    49   \item {\tt Addsplits}, \bold{18}
    49   \item {\tt Addsplits}, \bold{22}
    50   \item {\tt addsplits}, \bold{18}, 23, 35
    50   \item {\tt addsplits}, \bold{22}, 27, 39
    51   \item {\tt ALL} symbol, 2, 4, 11, 12, 56
    51   \item {\tt ALL} symbol, 6, 8, 15, 16, 59
    52   \item {\tt All} constant, 2, 56
    52   \item {\tt All} constant, 6, 59
    53   \item {\tt All_def} theorem, 6
    53   \item {\tt All_def} theorem, 10
    54   \item {\tt all_dupE} theorem, 8
    54   \item {\tt all_dupE} theorem, 12
    55   \item {\tt allE} theorem, 8
    55   \item {\tt allE} theorem, 12
    56   \item {\tt allI} theorem, 8
    56   \item {\tt allI} theorem, 12
    57   \item {\tt allL} theorem, 58, 62
    57   \item {\tt allL} theorem, 61, 65
    58   \item {\tt allL_thin} theorem, 59
    58   \item {\tt allL_thin} theorem, 62
    59   \item {\tt allR} theorem, 58
    59   \item {\tt allR} theorem, 61
    60   \item {\tt and_def} theorem, 6
    60   \item {\tt and_def} theorem, 10
    61   \item {\tt arg_cong} theorem, 7
    61   \item {\tt arg_cong} theorem, 11
    62   \item {\tt Arith} theory, 22, 79
    62   \item {\tt Arith} theory, 26, 82
    63   \item assumptions
    63   \item assumptions
    64     \subitem in {\CTT}, 68, 78
    64     \subitem in {\CTT}, 71, 81
    65 
    65 
    66   \indexspace
    66   \indexspace
    67 
    67 
    68   \item {\tt Ball} constant, 10, 12
    68   \item {\tt Ball} constant, 14, 16
    69   \item {\tt Ball_def} theorem, 13
    69   \item {\tt Ball_def} theorem, 17
    70   \item {\tt ballE} theorem, 14
    70   \item {\tt ballE} theorem, 18
    71   \item {\tt ballI} theorem, 14
    71   \item {\tt ballI} theorem, 18
    72   \item {\tt basic} theorem, 58
    72   \item {\tt basic} theorem, 61
    73   \item {\tt basic_defs}, \bold{76}
    73   \item {\tt basic_defs}, \bold{79}
    74   \item {\tt best_tac}, \bold{63}
    74   \item {\tt best_tac}, \bold{66}
    75   \item {\tt Bex} constant, 10, 12
    75   \item {\tt Bex} constant, 14, 16
    76   \item {\tt Bex_def} theorem, 13
    76   \item {\tt Bex_def} theorem, 17
    77   \item {\tt bexCI} theorem, 12, 14
    77   \item {\tt bexCI} theorem, 16, 18
    78   \item {\tt bexE} theorem, 14
    78   \item {\tt bexE} theorem, 18
    79   \item {\tt bexI} theorem, 12, 14
    79   \item {\tt bexI} theorem, 16, 18
    80   \item {\textit {bool}} type, 3
    80   \item {\textit {bool}} type, 7
    81   \item {\tt box_equals} theorem, 7, 9
    81   \item {\tt box_equals} theorem, 11, 13
    82   \item {\tt bspec} theorem, 14
    82   \item {\tt bspec} theorem, 18
    83   \item {\tt butlast} constant, 24
    83   \item {\tt butlast} constant, 28
    84 
    84 
    85   \indexspace
    85   \indexspace
    86 
    86 
    87   \item {\tt case} symbol, 5, 22, 23, 35
    87   \item {\tt case} symbol, 9, 26, 27, 39
    88   \item {\tt case_tac}, \bold{9}
    88   \item {\tt case_tac}, \bold{13}
    89   \item {\tt ccontr} theorem, 8
    89   \item {\tt CCL} theory, 1
    90   \item {\tt classical} theorem, 8
    90   \item {\tt ccontr} theorem, 12
    91   \item {\tt coinductive}, 47--50
    91   \item {\tt classical} theorem, 12
    92   \item {\tt Collect} constant, 10, 12
    92   \item {\tt coinductive}, 51--53
    93   \item {\tt Collect_mem_eq} theorem, 12, 13
    93   \item {\tt Collect} constant, 14, 16
    94   \item {\tt CollectD} theorem, 14, 53
    94   \item {\tt Collect_mem_eq} theorem, 16, 17
    95   \item {\tt CollectE} theorem, 14
    95   \item {\tt CollectD} theorem, 18, 56
    96   \item {\tt CollectI} theorem, 14, 53
    96   \item {\tt CollectE} theorem, 18
    97   \item {\tt comp_rls}, \bold{76}
    97   \item {\tt CollectI} theorem, 18, 57
    98   \item {\tt Compl} constant, 10
    98   \item {\tt comp_rls}, \bold{79}
    99   \item {\tt Compl_def} theorem, 13
    99   \item {\tt Compl} constant, 14
   100   \item {\tt Compl_disjoint} theorem, 16
   100   \item {\tt Compl_def} theorem, 17
   101   \item {\tt Compl_Int} theorem, 16
   101   \item {\tt Compl_disjoint} theorem, 20
   102   \item {\tt Compl_partition} theorem, 16
   102   \item {\tt Compl_Int} theorem, 20
   103   \item {\tt Compl_Un} theorem, 16
   103   \item {\tt Compl_partition} theorem, 20
   104   \item {\tt ComplD} theorem, 15
   104   \item {\tt Compl_Un} theorem, 20
   105   \item {\tt ComplI} theorem, 15
   105   \item {\tt ComplD} theorem, 19
   106   \item {\tt concat} constant, 24
   106   \item {\tt ComplI} theorem, 19
   107   \item {\tt cong} theorem, 7
   107   \item {\tt concat} constant, 28
   108   \item {\tt conj_cong}, 17
   108   \item {\tt cong} theorem, 11
   109   \item {\tt conjE} theorem, 7
   109   \item {\tt conj_cong}, 21
   110   \item {\tt conjI} theorem, 7
   110   \item {\tt conjE} theorem, 11
   111   \item {\tt conjL} theorem, 58
   111   \item {\tt conjI} theorem, 11
   112   \item {\tt conjR} theorem, 58
   112   \item {\tt conjL} theorem, 61
   113   \item {\tt conjunct1} theorem, 7
   113   \item {\tt conjR} theorem, 61
   114   \item {\tt conjunct2} theorem, 7
   114   \item {\tt conjunct1} theorem, 11
   115   \item {\tt conL} theorem, 59
   115   \item {\tt conjunct2} theorem, 11
   116   \item {\tt conR} theorem, 59
   116   \item {\tt conL} theorem, 62
   117   \item Constructive Type Theory, 68--90
   117   \item {\tt conR} theorem, 62
   118   \item {\tt contr} constant, 69
   118   \item Constructive Type Theory, 71--93
   119   \item {\tt could_res}, \bold{61}
   119   \item {\tt contr} constant, 72
   120   \item {\tt could_resolve_seq}, \bold{61}
   120   \item {\tt could_res}, \bold{64}
   121   \item {\tt CTT} theory, 68
   121   \item {\tt could_resolve_seq}, \bold{64}
   122   \item {\tt cut} theorem, 58
   122   \item {\tt CTT} theory, 1, 71
   123   \item {\tt cutL_tac}, \bold{60}
   123   \item {\tt Cube} theory, 1
   124   \item {\tt cutR_tac}, \bold{60}
   124   \item {\tt cut} theorem, 61
   125 
   125   \item {\tt cutL_tac}, \bold{63}
   126   \indexspace
   126   \item {\tt cutR_tac}, \bold{63}
   127 
   127 
   128   \item {\tt datatype}, 32--40
   128   \indexspace
   129   \item {\tt Delsplits}, \bold{18}
   129 
   130   \item {\tt delsplits}, \bold{18}
   130   \item {\tt datatype}, 36--44
   131   \item {\tt diff_0_eq_0} theorem, 80
   131   \item {\tt Delsplits}, \bold{22}
   132   \item {\tt diff_def} theorem, 80
   132   \item {\tt delsplits}, \bold{22}
   133   \item {\tt diff_self_eq_0} theorem, 80
   133   \item {\tt diff_0_eq_0} theorem, 83
   134   \item {\tt diff_succ_succ} theorem, 80
   134   \item {\tt diff_def} theorem, 83
   135   \item {\tt diff_typing} theorem, 80
   135   \item {\tt diff_self_eq_0} theorem, 83
   136   \item {\tt diffC0} theorem, 80
   136   \item {\tt diff_succ_succ} theorem, 83
   137   \item {\tt disjCI} theorem, 8
   137   \item {\tt diff_typing} theorem, 83
   138   \item {\tt disjE} theorem, 7
   138   \item {\tt diffC0} theorem, 83
   139   \item {\tt disjI1} theorem, 7
   139   \item {\tt disjCI} theorem, 12
   140   \item {\tt disjI2} theorem, 7
   140   \item {\tt disjE} theorem, 11
   141   \item {\tt disjL} theorem, 58
   141   \item {\tt disjI1} theorem, 11
   142   \item {\tt disjR} theorem, 58
   142   \item {\tt disjI2} theorem, 11
   143   \item {\tt div} symbol, 21, 80
   143   \item {\tt disjL} theorem, 61
   144   \item {\tt div_def} theorem, 80
   144   \item {\tt disjR} theorem, 61
   145   \item {\tt div_geq} theorem, 22
   145   \item {\tt div} symbol, 25, 83
   146   \item {\tt div_less} theorem, 22
   146   \item {\tt div_def} theorem, 83
   147   \item {\tt Divides} theory, 22
   147   \item {\tt div_geq} theorem, 26
   148   \item {\tt double_complement} theorem, 16
   148   \item {\tt div_less} theorem, 26
   149   \item {\tt drop} constant, 24
   149   \item {\tt Divides} theory, 26
   150   \item {\tt dropWhile} constant, 24
   150   \item {\tt double_complement} theorem, 20
   151 
   151   \item {\tt drop} constant, 28
   152   \indexspace
   152   \item {\tt dropWhile} constant, 28
   153 
   153 
   154   \item {\tt Elem} constant, 69
   154   \indexspace
   155   \item {\tt elim_rls}, \bold{76}
   155 
   156   \item {\tt elimL_rls}, \bold{76}
   156   \item {\tt Elem} constant, 72
   157   \item {\tt empty_def} theorem, 13
   157   \item {\tt elim_rls}, \bold{79}
   158   \item {\tt empty_pack}, \bold{62}
   158   \item {\tt elimL_rls}, \bold{79}
   159   \item {\tt emptyE} theorem, 15
   159   \item {\tt empty_def} theorem, 17
   160   \item {\tt Eps} constant, 2, 4
   160   \item {\tt empty_pack}, \bold{65}
   161   \item {\tt Eq} constant, 69
   161   \item {\tt emptyE} theorem, 19
   162   \item {\tt eq} constant, 69, 74
   162   \item {\tt Eps} constant, 6, 8
   163   \item {\tt EqC} theorem, 75
   163   \item {\tt Eq} constant, 72
   164   \item {\tt EqE} theorem, 75
   164   \item {\tt eq} constant, 72, 77
   165   \item {\tt Eqelem} constant, 69
   165   \item {\tt EqC} theorem, 78
   166   \item {\tt EqF} theorem, 75
   166   \item {\tt EqE} theorem, 78
   167   \item {\tt EqFL} theorem, 75
   167   \item {\tt Eqelem} constant, 72
   168   \item {\tt EqI} theorem, 75
   168   \item {\tt EqF} theorem, 78
   169   \item {\tt Eqtype} constant, 69
   169   \item {\tt EqFL} theorem, 78
   170   \item {\tt equal_tac}, \bold{77}
   170   \item {\tt EqI} theorem, 78
   171   \item {\tt equal_types} theorem, 72
   171   \item {\tt Eqtype} constant, 72
   172   \item {\tt equal_typesL} theorem, 72
   172   \item {\tt equal_tac}, \bold{80}
   173   \item {\tt equalityCE} theorem, 12, 14, 53, 54
   173   \item {\tt equal_types} theorem, 75
   174   \item {\tt equalityD1} theorem, 14
   174   \item {\tt equal_typesL} theorem, 75
   175   \item {\tt equalityD2} theorem, 14
   175   \item {\tt equalityCE} theorem, 16, 18, 56, 57
   176   \item {\tt equalityE} theorem, 14
   176   \item {\tt equalityD1} theorem, 18
   177   \item {\tt equalityI} theorem, 14
   177   \item {\tt equalityD2} theorem, 18
   178   \item {\tt EX} symbol, 2, 4, 11, 12, 56
   178   \item {\tt equalityE} theorem, 18
   179   \item {\tt Ex} constant, 2, 56
   179   \item {\tt equalityI} theorem, 18
   180   \item {\tt EX!} symbol, 2
   180   \item {\tt EX} symbol, 6, 8, 15, 16, 59
   181   \item {\tt Ex1} constant, 2
   181   \item {\tt Ex} constant, 6, 59
   182   \item {\tt Ex1_def} theorem, 6
   182   \item {\tt EX!} symbol, 6
   183   \item {\tt ex1E} theorem, 8
   183   \item {\tt Ex1} constant, 6
   184   \item {\tt ex1I} theorem, 8
   184   \item {\tt Ex1_def} theorem, 10
   185   \item {\tt Ex_def} theorem, 6
   185   \item {\tt ex1E} theorem, 12
   186   \item {\tt exCI} theorem, 8
   186   \item {\tt ex1I} theorem, 12
   187   \item {\tt excluded_middle} theorem, 8
   187   \item {\tt Ex_def} theorem, 10
   188   \item {\tt exE} theorem, 8
   188   \item {\tt exCI} theorem, 12
   189   \item {\tt exhaust_tac}, \bold{36}
   189   \item {\tt excluded_middle} theorem, 12
   190   \item {\tt exI} theorem, 8
   190   \item {\tt exE} theorem, 12
   191   \item {\tt exL} theorem, 58
   191   \item {\tt exhaust_tac}, \bold{40}
   192   \item {\tt Exp} theory, 51
   192   \item {\tt exI} theorem, 12
   193   \item {\tt exR} theorem, 58, 62, 64
   193   \item {\tt exL} theorem, 61
   194   \item {\tt exR_thin} theorem, 59, 64, 65
   194   \item {\tt Exp} theory, 55
   195   \item {\tt ext} theorem, 5, 6
   195   \item {\tt exR} theorem, 61, 65, 67
   196 
   196   \item {\tt exR_thin} theorem, 62, 67, 68
   197   \indexspace
   197   \item {\tt ext} theorem, 9, 10
   198 
   198 
   199   \item {\tt F} constant, 69
   199   \indexspace
   200   \item {\tt False} constant, 2, 56
   200 
   201   \item {\tt False_def} theorem, 6
   201   \item {\tt F} constant, 72
   202   \item {\tt FalseE} theorem, 7
   202   \item {\tt False} constant, 6, 59
   203   \item {\tt FalseL} theorem, 58
   203   \item {\tt False_def} theorem, 10
   204   \item {\tt fast_tac}, \bold{63}
   204   \item {\tt FalseE} theorem, 11
   205   \item {\tt FE} theorem, 75, 79
   205   \item {\tt FalseL} theorem, 61
   206   \item {\tt FEL} theorem, 75
   206   \item {\tt fast_tac}, \bold{66}
   207   \item {\tt FF} theorem, 75
   207   \item {\tt FE} theorem, 78, 82
   208   \item {\tt filseq_resolve_tac}, \bold{61}
   208   \item {\tt FEL} theorem, 78
   209   \item {\tt filt_resolve_tac}, 61, 77
   209   \item {\tt FF} theorem, 78
   210   \item {\tt filter} constant, 24
   210   \item {\tt filseq_resolve_tac}, \bold{64}
   211   \item flex-flex constraints, 57
   211   \item {\tt filt_resolve_tac}, 64, 80
   212   \item {\tt FOL} theory, 78
   212   \item {\tt filter} constant, 28
   213   \item {\tt foldl} constant, 24
   213   \item flex-flex constraints, 60
   214   \item {\tt form_rls}, \bold{76}
   214   \item {\tt FOL} theory, 81
   215   \item {\tt formL_rls}, \bold{76}
   215   \item {\tt foldl} constant, 28
   216   \item {\tt forms_of_seq}, \bold{60}
   216   \item {\tt form_rls}, \bold{79}
   217   \item {\tt fst} constant, 19, 69, 74
   217   \item {\tt formL_rls}, \bold{79}
   218   \item {\tt fst_conv} theorem, 19
   218   \item {\tt forms_of_seq}, \bold{63}
   219   \item {\tt fst_def} theorem, 74
   219   \item {\tt fst} constant, 23, 72, 77
   220   \item {\tt Fun} theory, 17
   220   \item {\tt fst_conv} theorem, 23
   221   \item {\textit {fun}} type, 3
   221   \item {\tt fst_def} theorem, 77
   222   \item {\tt fun_cong} theorem, 7
   222   \item {\tt Fun} theory, 21
       
   223   \item {\textit {fun}} type, 7
       
   224   \item {\tt fun_cong} theorem, 11
   223   \item function applications
   225   \item function applications
   224     \subitem in \CTT, 71
   226     \subitem in \CTT, 74
   225 
   227 
   226   \indexspace
   228   \indexspace
   227 
   229 
   228   \item {\tt hd} constant, 24
   230   \item {\tt hd} constant, 28
   229   \item higher-order logic, 1--54
   231   \item higher-order logic, 5--57
   230   \item {\tt HOL} theory, 1
   232   \item {\tt HOL} theory, 1, 5
   231   \item {\sc hol} system, 1, 4
   233   \item {\sc hol} system, 5, 8
   232   \item {\tt HOL_basic_ss}, \bold{17}
   234   \item {\tt HOL_basic_ss}, \bold{21}
   233   \item {\tt HOL_cs}, \bold{18}
   235   \item {\tt HOL_cs}, \bold{22}
   234   \item {\tt HOL_quantifiers}, \bold{4}, 12
   236   \item {\tt HOL_quantifiers}, \bold{8}, 16
   235   \item {\tt HOL_ss}, \bold{17}
   237   \item {\tt HOL_ss}, \bold{21}
   236   \item {\tt hyp_rew_tac}, \bold{78}
   238   \item {\tt HOLCF} theory, 1
   237   \item {\tt hyp_subst_tac}, 17
   239   \item {\tt hyp_rew_tac}, \bold{81}
   238 
   240   \item {\tt hyp_subst_tac}, 21
   239   \indexspace
   241 
   240 
   242   \indexspace
   241   \item {\textit {i}} type, 68
   243 
   242   \item {\tt If} constant, 2
   244   \item {\textit {i}} type, 71
   243   \item {\tt if_def} theorem, 6
   245   \item {\tt If} constant, 6
   244   \item {\tt if_not_P} theorem, 8
   246   \item {\tt if_def} theorem, 10
   245   \item {\tt if_P} theorem, 8
   247   \item {\tt if_not_P} theorem, 12
   246   \item {\tt iff} theorem, 5, 6
   248   \item {\tt if_P} theorem, 12
   247   \item {\tt iff_def} theorem, 58
   249   \item {\tt iff} theorem, 9, 10
   248   \item {\tt iffCE} theorem, 8, 12
   250   \item {\tt iff_def} theorem, 61
   249   \item {\tt iffD1} theorem, 7
   251   \item {\tt iffCE} theorem, 12, 16
   250   \item {\tt iffD2} theorem, 7
   252   \item {\tt iffD1} theorem, 11
   251   \item {\tt iffE} theorem, 7
   253   \item {\tt iffD2} theorem, 11
   252   \item {\tt iffI} theorem, 7
   254   \item {\tt iffE} theorem, 11
   253   \item {\tt iffL} theorem, 59, 66
   255   \item {\tt iffI} theorem, 11
   254   \item {\tt iffR} theorem, 59
   256   \item {\tt iffL} theorem, 62, 69
   255   \item {\tt image_def} theorem, 13
   257   \item {\tt iffR} theorem, 62
   256   \item {\tt imageE} theorem, 15
   258   \item {\tt ILL} theory, 1
   257   \item {\tt imageI} theorem, 15
   259   \item {\tt image_def} theorem, 17
   258   \item {\tt impCE} theorem, 8
   260   \item {\tt imageE} theorem, 19
   259   \item {\tt impE} theorem, 7
   261   \item {\tt imageI} theorem, 19
   260   \item {\tt impI} theorem, 5
   262   \item {\tt impCE} theorem, 12
   261   \item {\tt impL} theorem, 58
   263   \item {\tt impE} theorem, 11
   262   \item {\tt impR} theorem, 58
   264   \item {\tt impI} theorem, 9
   263   \item {\tt in} symbol, 3
   265   \item {\tt impL} theorem, 61
   264   \item {\textit {ind}} type, 20
   266   \item {\tt impR} theorem, 61
   265   \item {\tt induct_tac}, 22, \bold{36}
   267   \item {\tt in} symbol, 7
   266   \item {\tt inductive}, 47--50
   268   \item {\textit {ind}} type, 24
   267   \item {\tt inj} constant, 17
   269   \item {\tt induct_tac}, 26, \bold{40}
   268   \item {\tt inj_def} theorem, 17
   270   \item {\tt inductive}, 51--53
   269   \item {\tt inj_Inl} theorem, 21
   271   \item {\tt inj} constant, 21
   270   \item {\tt inj_Inr} theorem, 21
   272   \item {\tt inj_def} theorem, 21
   271   \item {\tt inj_on} constant, 17
   273   \item {\tt inj_Inl} theorem, 25
   272   \item {\tt inj_on_def} theorem, 17
   274   \item {\tt inj_Inr} theorem, 25
   273   \item {\tt inj_Suc} theorem, 21
   275   \item {\tt inj_on} constant, 21
   274   \item {\tt Inl} constant, 21
   276   \item {\tt inj_on_def} theorem, 21
   275   \item {\tt inl} constant, 69, 74, 84
   277   \item {\tt inj_Suc} theorem, 25
   276   \item {\tt Inl_not_Inr} theorem, 21
   278   \item {\tt Inl} constant, 25
   277   \item {\tt Inr} constant, 21
   279   \item {\tt inl} constant, 72, 77, 87
   278   \item {\tt inr} constant, 69, 74
   280   \item {\tt Inl_not_Inr} theorem, 25
   279   \item {\tt insert} constant, 10
   281   \item {\tt Inr} constant, 25
   280   \item {\tt insert_def} theorem, 13
   282   \item {\tt inr} constant, 72, 77
   281   \item {\tt insertE} theorem, 15
   283   \item {\tt insert} constant, 14
   282   \item {\tt insertI1} theorem, 15
   284   \item {\tt insert_def} theorem, 17
   283   \item {\tt insertI2} theorem, 15
   285   \item {\tt insertE} theorem, 19
   284   \item {\tt INT} symbol, 10--12
   286   \item {\tt insertI1} theorem, 19
   285   \item {\tt Int} symbol, 10
   287   \item {\tt insertI2} theorem, 19
   286   \item {\tt Int_absorb} theorem, 16
   288   \item {\tt INT} symbol, 14--16
   287   \item {\tt Int_assoc} theorem, 16
   289   \item {\tt Int} symbol, 14
   288   \item {\tt Int_commute} theorem, 16
   290   \item {\tt Int_absorb} theorem, 20
   289   \item {\tt INT_D} theorem, 15
   291   \item {\tt Int_assoc} theorem, 20
   290   \item {\tt Int_def} theorem, 13
   292   \item {\tt Int_commute} theorem, 20
   291   \item {\tt INT_E} theorem, 15
   293   \item {\tt INT_D} theorem, 19
   292   \item {\tt Int_greatest} theorem, 16
   294   \item {\tt Int_def} theorem, 17
   293   \item {\tt INT_I} theorem, 15
   295   \item {\tt INT_E} theorem, 19
   294   \item {\tt Int_Inter_image} theorem, 16
   296   \item {\tt Int_greatest} theorem, 20
   295   \item {\tt Int_lower1} theorem, 16
   297   \item {\tt INT_I} theorem, 19
   296   \item {\tt Int_lower2} theorem, 16
   298   \item {\tt Int_Inter_image} theorem, 20
   297   \item {\tt Int_Un_distrib} theorem, 16
   299   \item {\tt Int_lower1} theorem, 20
   298   \item {\tt Int_Union} theorem, 16
   300   \item {\tt Int_lower2} theorem, 20
   299   \item {\tt IntD1} theorem, 15
   301   \item {\tt Int_Un_distrib} theorem, 20
   300   \item {\tt IntD2} theorem, 15
   302   \item {\tt Int_Union} theorem, 20
   301   \item {\tt IntE} theorem, 15
   303   \item {\tt IntD1} theorem, 19
   302   \item {\tt INTER} constant, 10
   304   \item {\tt IntD2} theorem, 19
   303   \item {\tt Inter} constant, 10
   305   \item {\tt IntE} theorem, 19
   304   \item {\tt INTER1} constant, 10
   306   \item {\tt INTER} constant, 14
   305   \item {\tt INTER1_def} theorem, 13
   307   \item {\tt Inter} constant, 14
   306   \item {\tt INTER_def} theorem, 13
   308   \item {\tt INTER1} constant, 14
   307   \item {\tt Inter_def} theorem, 13
   309   \item {\tt INTER1_def} theorem, 17
   308   \item {\tt Inter_greatest} theorem, 16
   310   \item {\tt INTER_def} theorem, 17
   309   \item {\tt Inter_lower} theorem, 16
   311   \item {\tt Inter_def} theorem, 17
   310   \item {\tt Inter_Un_distrib} theorem, 16
   312   \item {\tt Inter_greatest} theorem, 20
   311   \item {\tt InterD} theorem, 15
   313   \item {\tt Inter_lower} theorem, 20
   312   \item {\tt InterE} theorem, 15
   314   \item {\tt Inter_Un_distrib} theorem, 20
   313   \item {\tt InterI} theorem, 15
   315   \item {\tt InterD} theorem, 19
   314   \item {\tt IntI} theorem, 15
   316   \item {\tt InterE} theorem, 19
   315   \item {\tt intr_rls}, \bold{76}
   317   \item {\tt InterI} theorem, 19
   316   \item {\tt intr_tac}, \bold{77}, 86, 87
   318   \item {\tt IntI} theorem, 19
   317   \item {\tt intrL_rls}, \bold{76}
   319   \item {\tt intr_rls}, \bold{79}
   318   \item {\tt inv} constant, 17
   320   \item {\tt intr_tac}, \bold{80}, 89, 90
   319   \item {\tt inv_def} theorem, 17
   321   \item {\tt intrL_rls}, \bold{79}
   320 
   322   \item {\tt inv} constant, 21
   321   \indexspace
   323   \item {\tt inv_def} theorem, 21
   322 
   324 
   323   \item {\tt lam} symbol, 71
   325   \indexspace
   324   \item {\tt lambda} constant, 69, 71
   326 
       
   327   \item {\tt lam} symbol, 74
       
   328   \item {\tt lambda} constant, 72, 74
   325   \item $\lambda$-abstractions
   329   \item $\lambda$-abstractions
   326     \subitem in \CTT, 71
   330     \subitem in \CTT, 74
   327   \item {\tt last} constant, 24
   331   \item {\tt last} constant, 28
   328   \item {\tt LEAST} constant, 3, 4, 22
   332   \item {\tt LCF} theory, 1
   329   \item {\tt Least} constant, 2
   333   \item {\tt LEAST} constant, 7, 8, 26
   330   \item {\tt Least_def} theorem, 6
   334   \item {\tt Least} constant, 6
   331   \item {\tt length} constant, 24
   335   \item {\tt Least_def} theorem, 10
   332   \item {\tt less_induct} theorem, 23
   336   \item {\tt length} constant, 28
   333   \item {\tt Let} constant, 2, 5
   337   \item {\tt less_induct} theorem, 27
   334   \item {\tt let} symbol, 3, 5
   338   \item {\tt Let} constant, 6, 9
   335   \item {\tt Let_def} theorem, 5, 6
   339   \item {\tt let} symbol, 7, 9
   336   \item {\tt LFilter} theory, 51
   340   \item {\tt Let_def} theorem, 9, 10
   337   \item {\tt List} theory, 23, 24
   341   \item {\tt LFilter} theory, 55
   338   \item {\textit{list}} type, 23
   342   \item {\tt List} theory, 27, 28
   339   \item {\tt LK} theory, 55, 59
   343   \item {\textit{list}} type, 27
   340   \item {\tt LK_dup_pack}, \bold{62}, 63
   344   \item {\tt LK} theory, 1, 58, 62
   341   \item {\tt LK_pack}, \bold{62}
   345   \item {\tt LK_dup_pack}, \bold{65}, 66
   342   \item {\tt LList} theory, 51
   346   \item {\tt LK_pack}, \bold{65}
   343 
   347   \item {\tt LList} theory, 54
   344   \indexspace
   348 
   345 
   349   \indexspace
   346   \item {\tt map} constant, 24
   350 
   347   \item {\tt max} constant, 3, 22
   351   \item {\tt map} constant, 28
   348   \item {\tt mem} symbol, 24
   352   \item {\tt max} constant, 7, 26
   349   \item {\tt mem_Collect_eq} theorem, 12, 13
   353   \item {\tt mem} symbol, 28
   350   \item {\tt min} constant, 3, 22
   354   \item {\tt mem_Collect_eq} theorem, 16, 17
   351   \item {\tt minus} class, 3
   355   \item {\tt min} constant, 7, 26
   352   \item {\tt mod} symbol, 21, 80
   356   \item {\tt minus} class, 7
   353   \item {\tt mod_def} theorem, 80
   357   \item {\tt mod} symbol, 25, 83
   354   \item {\tt mod_geq} theorem, 22
   358   \item {\tt mod_def} theorem, 83
   355   \item {\tt mod_less} theorem, 22
   359   \item {\tt mod_geq} theorem, 26
   356   \item {\tt mono} constant, 3
   360   \item {\tt mod_less} theorem, 26
   357   \item {\tt mp} theorem, 5
   361   \item {\tt Modal} theory, 1
   358   \item {\tt mp_tac}, \bold{78}
   362   \item {\tt mono} constant, 7
   359   \item {\tt mult_assoc} theorem, 80
   363   \item {\tt mp} theorem, 9
   360   \item {\tt mult_commute} theorem, 80
   364   \item {\tt mp_tac}, \bold{81}
   361   \item {\tt mult_def} theorem, 80
   365   \item {\tt mult_assoc} theorem, 83
   362   \item {\tt mult_typing} theorem, 80
   366   \item {\tt mult_commute} theorem, 83
   363   \item {\tt multC0} theorem, 80
   367   \item {\tt mult_def} theorem, 83
   364   \item {\tt multC_succ} theorem, 80
   368   \item {\tt mult_typing} theorem, 83
   365   \item {\tt mutual_induct_tac}, \bold{36}
   369   \item {\tt multC0} theorem, 83
   366 
   370   \item {\tt multC_succ} theorem, 83
   367   \indexspace
   371   \item {\tt mutual_induct_tac}, \bold{40}
   368 
   372 
   369   \item {\tt N} constant, 69
   373   \indexspace
   370   \item {\tt n_not_Suc_n} theorem, 21
   374 
   371   \item {\tt Nat} theory, 22
   375   \item {\tt N} constant, 72
   372   \item {\textit {nat}} type, 21, 22
   376   \item {\tt n_not_Suc_n} theorem, 25
   373   \item {\textit{nat}} type, 20--23
   377   \item {\tt Nat} theory, 26
   374   \item {\tt nat_induct} theorem, 21
   378   \item {\textit {nat}} type, 25, 26
   375   \item {\tt nat_rec} constant, 22
   379   \item {\textit{nat}} type, 24--27
   376   \item {\tt NatDef} theory, 20
   380   \item {\tt nat_induct} theorem, 25
   377   \item {\tt NC0} theorem, 73
   381   \item {\tt nat_rec} constant, 26
   378   \item {\tt NC_succ} theorem, 73
   382   \item {\tt NatDef} theory, 24
   379   \item {\tt NE} theorem, 72, 73, 81
   383   \item {\tt NC0} theorem, 76
   380   \item {\tt NEL} theorem, 73
   384   \item {\tt NC_succ} theorem, 76
   381   \item {\tt NF} theorem, 73, 82
   385   \item {\tt NE} theorem, 75, 76, 84
   382   \item {\tt NI0} theorem, 73
   386   \item {\tt NEL} theorem, 76
   383   \item {\tt NI_succ} theorem, 73
   387   \item {\tt NF} theorem, 76, 85
   384   \item {\tt NI_succL} theorem, 73
   388   \item {\tt NI0} theorem, 76
   385   \item {\tt NIO} theorem, 81
   389   \item {\tt NI_succ} theorem, 76
   386   \item {\tt Not} constant, 2, 56
   390   \item {\tt NI_succL} theorem, 76
   387   \item {\tt not_def} theorem, 6
   391   \item {\tt NIO} theorem, 84
   388   \item {\tt not_sym} theorem, 7
   392   \item {\tt Not} constant, 6, 59
   389   \item {\tt notE} theorem, 7
   393   \item {\tt not_def} theorem, 10
   390   \item {\tt notI} theorem, 7
   394   \item {\tt not_sym} theorem, 11
   391   \item {\tt notL} theorem, 58
   395   \item {\tt notE} theorem, 11
   392   \item {\tt notnotD} theorem, 8
   396   \item {\tt notI} theorem, 11
   393   \item {\tt notR} theorem, 58
   397   \item {\tt notL} theorem, 61
   394   \item {\tt null} constant, 24
   398   \item {\tt notnotD} theorem, 12
   395 
   399   \item {\tt notR} theorem, 61
   396   \indexspace
   400   \item {\tt null} constant, 28
   397 
   401 
   398   \item {\textit {o}} type, 55
   402   \indexspace
   399   \item {\tt o} symbol, 2, 13
   403 
   400   \item {\tt o_def} theorem, 6
   404   \item {\textit {o}} type, 58
   401   \item {\tt of} symbol, 5
   405   \item {\tt o} symbol, 6, 17
   402   \item {\tt or_def} theorem, 6
   406   \item {\tt o_def} theorem, 10
   403   \item {\tt Ord} theory, 3
   407   \item {\tt of} symbol, 9
   404   \item {\tt ord} class, 3, 4, 22
   408   \item {\tt or_def} theorem, 10
   405   \item {\tt order} class, 3, 22
   409   \item {\tt Ord} theory, 7
   406 
   410   \item {\tt ord} class, 7, 8, 26
   407   \indexspace
   411   \item {\tt order} class, 7, 26
   408 
   412 
   409   \item {\tt pack} ML type, 61
   413   \indexspace
   410   \item {\tt Pair} constant, 19
   414 
   411   \item {\tt pair} constant, 69
   415   \item {\tt pack} ML type, 64
   412   \item {\tt Pair_eq} theorem, 19
   416   \item {\tt Pair} constant, 23
   413   \item {\tt Pair_inject} theorem, 19
   417   \item {\tt pair} constant, 72
   414   \item {\tt PairE} theorem, 19
   418   \item {\tt Pair_eq} theorem, 23
   415   \item {\tt pc_tac}, \bold{63}, \bold{79}, 85, 86
   419   \item {\tt Pair_inject} theorem, 23
   416   \item {\tt plus} class, 3
   420   \item {\tt PairE} theorem, 23
   417   \item {\tt PlusC_inl} theorem, 75
   421   \item {\tt pc_tac}, \bold{66}, \bold{82}, 88, 89
   418   \item {\tt PlusC_inr} theorem, 75
   422   \item {\tt plus} class, 7
   419   \item {\tt PlusE} theorem, 75, 79, 83
   423   \item {\tt PlusC_inl} theorem, 78
   420   \item {\tt PlusEL} theorem, 75
   424   \item {\tt PlusC_inr} theorem, 78
   421   \item {\tt PlusF} theorem, 75
   425   \item {\tt PlusE} theorem, 78, 82, 86
   422   \item {\tt PlusFL} theorem, 75
   426   \item {\tt PlusEL} theorem, 78
   423   \item {\tt PlusI_inl} theorem, 75, 84
   427   \item {\tt PlusF} theorem, 78
   424   \item {\tt PlusI_inlL} theorem, 75
   428   \item {\tt PlusFL} theorem, 78
   425   \item {\tt PlusI_inr} theorem, 75
   429   \item {\tt PlusI_inl} theorem, 78, 87
   426   \item {\tt PlusI_inrL} theorem, 75
   430   \item {\tt PlusI_inlL} theorem, 78
   427   \item {\tt Pow} constant, 10
   431   \item {\tt PlusI_inr} theorem, 78
   428   \item {\tt Pow_def} theorem, 13
   432   \item {\tt PlusI_inrL} theorem, 78
   429   \item {\tt PowD} theorem, 15
   433   \item {\tt Pow} constant, 14
   430   \item {\tt PowI} theorem, 15
   434   \item {\tt Pow_def} theorem, 17
   431   \item {\tt primrec}, 41--44
   435   \item {\tt PowD} theorem, 19
   432   \item {\tt primrec} symbol, 22
   436   \item {\tt PowI} theorem, 19
   433   \item {\tt PROD} symbol, 70, 71
   437   \item {\tt primrec}, 45--48
   434   \item {\tt Prod} constant, 69
   438   \item {\tt primrec} symbol, 26
   435   \item {\tt Prod} theory, 19
   439   \item priorities, 3
   436   \item {\tt ProdC} theorem, 73, 89
   440   \item {\tt PROD} symbol, 73, 74
   437   \item {\tt ProdC2} theorem, 73
   441   \item {\tt Prod} constant, 72
   438   \item {\tt ProdE} theorem, 73, 86, 88, 90
   442   \item {\tt Prod} theory, 23
   439   \item {\tt ProdEL} theorem, 73
   443   \item {\tt ProdC} theorem, 76, 92
   440   \item {\tt ProdF} theorem, 73
   444   \item {\tt ProdC2} theorem, 76
   441   \item {\tt ProdFL} theorem, 73
   445   \item {\tt ProdE} theorem, 76, 89, 91, 93
   442   \item {\tt ProdI} theorem, 73, 79, 81
   446   \item {\tt ProdEL} theorem, 76
   443   \item {\tt ProdIL} theorem, 73
   447   \item {\tt ProdF} theorem, 76
   444   \item {\tt prop_cs}, \bold{18}
   448   \item {\tt ProdFL} theorem, 76
   445   \item {\tt prop_pack}, \bold{62}
   449   \item {\tt ProdI} theorem, 76, 82, 84
   446 
   450   \item {\tt ProdIL} theorem, 76
   447   \indexspace
   451   \item {\tt prop_cs}, \bold{22}
   448 
   452   \item {\tt prop_pack}, \bold{65}
   449   \item {\tt qed_spec_mp}, 39
   453 
   450 
   454   \indexspace
   451   \indexspace
   455 
   452 
   456   \item {\tt qed_spec_mp}, 43
   453   \item {\tt range} constant, 10, 52
   457 
   454   \item {\tt range_def} theorem, 13
   458   \indexspace
   455   \item {\tt rangeE} theorem, 15, 53
   459 
   456   \item {\tt rangeI} theorem, 15
   460   \item {\tt range} constant, 14, 56
   457   \item {\tt rec} constant, 69, 72
   461   \item {\tt range_def} theorem, 17
   458   \item {\tt recdef}, 44--47
   462   \item {\tt rangeE} theorem, 19, 56
   459   \item {\tt record}, 29
   463   \item {\tt rangeI} theorem, 19
   460   \item {\tt record_split_tac}, 31, 32
   464   \item {\tt rec} constant, 72, 75
       
   465   \item {\tt recdef}, 48--51
       
   466   \item {\tt record}, 33
       
   467   \item {\tt record_split_tac}, 35, 36
   461   \item recursion
   468   \item recursion
   462     \subitem general, 44--47
   469     \subitem general, 48--51
   463     \subitem primitive, 41--44
   470     \subitem primitive, 45--48
   464   \item recursive functions, \see{recursion}{40}
   471   \item recursive functions, \see{recursion}{44}
   465   \item {\tt red_if_equal} theorem, 72
   472   \item {\tt red_if_equal} theorem, 75
   466   \item {\tt Reduce} constant, 69, 72, 78
   473   \item {\tt Reduce} constant, 72, 75, 81
   467   \item {\tt refl} theorem, 5, 58
   474   \item {\tt refl} theorem, 9, 61
   468   \item {\tt refl_elem} theorem, 72, 76
   475   \item {\tt refl_elem} theorem, 75, 79
   469   \item {\tt refl_red} theorem, 72
   476   \item {\tt refl_red} theorem, 75
   470   \item {\tt refl_type} theorem, 72, 76
   477   \item {\tt refl_type} theorem, 75, 79
   471   \item {\tt REPEAT_FIRST}, 77
   478   \item {\tt REPEAT_FIRST}, 80
   472   \item {\tt repeat_goal_tac}, \bold{63}
   479   \item {\tt repeat_goal_tac}, \bold{66}
   473   \item {\tt replace_type} theorem, 76, 88
   480   \item {\tt replace_type} theorem, 79, 91
   474   \item {\tt reresolve_tac}, \bold{63}
   481   \item {\tt reresolve_tac}, \bold{66}
   475   \item {\tt res_inst_tac}, 4
   482   \item {\tt res_inst_tac}, 8
   476   \item {\tt rev} constant, 24
   483   \item {\tt rev} constant, 28
   477   \item {\tt rew_tac}, \bold{78}
   484   \item {\tt rew_tac}, \bold{81}
   478   \item {\tt RL}, 83
   485   \item {\tt RL}, 86
   479   \item {\tt RS}, 88, 90
   486   \item {\tt RS}, 91, 93
   480 
   487 
   481   \indexspace
   488   \indexspace
   482 
   489 
   483   \item {\tt safe_goal_tac}, \bold{63}
   490   \item {\tt safe_goal_tac}, \bold{66}
   484   \item {\tt safe_tac}, \bold{79}
   491   \item {\tt safe_tac}, \bold{82}
   485   \item {\tt safestep_tac}, \bold{79}
   492   \item {\tt safestep_tac}, \bold{82}
   486   \item search
   493   \item search
   487     \subitem best-first, 54
   494     \subitem best-first, 57
   488   \item {\tt select_equality} theorem, 6, 8
   495   \item {\tt select_equality} theorem, 10, 12
   489   \item {\tt selectI} theorem, 5, 6
   496   \item {\tt selectI} theorem, 9, 10
   490   \item {\tt Seqof} constant, 56
   497   \item {\tt Seqof} constant, 59
   491   \item sequent calculus, 55--67
   498   \item sequent calculus, 58--70
   492   \item {\tt Set} theory, 9, 12
   499   \item {\tt Set} theory, 13, 16
   493   \item {\tt set} constant, 24
   500   \item {\tt set} constant, 28
   494   \item {\tt set} type, 9
   501   \item {\tt set} type, 13
   495   \item {\tt set_current_thy}, 54
   502   \item {\tt set_current_thy}, 57
   496   \item {\tt set_diff_def} theorem, 13
   503   \item {\tt set_diff_def} theorem, 17
   497   \item {\tt show_sorts}, 4
   504   \item {\tt show_sorts}, 8
   498   \item {\tt show_types}, 4
   505   \item {\tt show_types}, 8
   499   \item {\tt Sigma} constant, 19
   506   \item {\tt Sigma} constant, 23
   500   \item {\tt Sigma_def} theorem, 19
   507   \item {\tt Sigma_def} theorem, 23
   501   \item {\tt SigmaE} theorem, 19
   508   \item {\tt SigmaE} theorem, 23
   502   \item {\tt SigmaI} theorem, 19
   509   \item {\tt SigmaI} theorem, 23
   503   \item simplification
   510   \item simplification
   504     \subitem of conjunctions, 17
   511     \subitem of conjunctions, 21
   505   \item {\tt size} constant, 35
   512   \item {\tt size} constant, 40
   506   \item {\tt snd} constant, 19, 69, 74
   513   \item {\tt snd} constant, 23, 72, 77
   507   \item {\tt snd_conv} theorem, 19
   514   \item {\tt snd_conv} theorem, 23
   508   \item {\tt snd_def} theorem, 74
   515   \item {\tt snd_def} theorem, 77
   509   \item {\tt sobj} type, 59
   516   \item {\tt sobj} type, 62
   510   \item {\tt spec} theorem, 8
   517   \item {\tt spec} theorem, 12
   511   \item {\tt split} constant, 19, 69, 83
   518   \item {\tt split} constant, 23, 72, 86
   512   \item {\tt split} theorem, 19
   519   \item {\tt split} theorem, 23
   513   \item {\tt split_all_tac}, \bold{20}
   520   \item {\tt split_all_tac}, \bold{24}
   514   \item {\tt split_if} theorem, 8, 18
   521   \item {\tt split_if} theorem, 12, 22
   515   \item {\tt split_list_case} theorem, 23
   522   \item {\tt split_list_case} theorem, 27
   516   \item {\tt split_split} theorem, 19
   523   \item {\tt split_split} theorem, 23
   517   \item {\tt split_sum_case} theorem, 21
   524   \item {\tt split_sum_case} theorem, 25
   518   \item {\tt ssubst} theorem, 7, 9
   525   \item {\tt ssubst} theorem, 11, 13
   519   \item {\tt stac}, \bold{17}
   526   \item {\tt stac}, \bold{21}
   520   \item {\tt step_tac}, \bold{63}, \bold{79}
   527   \item {\tt step_tac}, \bold{66}, \bold{82}
   521   \item {\tt strip_tac}, \bold{9}
   528   \item {\tt strip_tac}, \bold{13}
   522   \item {\tt subset_def} theorem, 13
   529   \item {\tt subset_def} theorem, 17
   523   \item {\tt subset_refl} theorem, 14
   530   \item {\tt subset_refl} theorem, 18
   524   \item {\tt subset_trans} theorem, 14
   531   \item {\tt subset_trans} theorem, 18
   525   \item {\tt subsetCE} theorem, 12, 14
   532   \item {\tt subsetCE} theorem, 16, 18
   526   \item {\tt subsetD} theorem, 12, 14
   533   \item {\tt subsetD} theorem, 16, 18
   527   \item {\tt subsetI} theorem, 14
   534   \item {\tt subsetI} theorem, 18
   528   \item {\tt subst} theorem, 5
   535   \item {\tt subst} theorem, 9
   529   \item {\tt subst_elem} theorem, 72
   536   \item {\tt subst_elem} theorem, 75
   530   \item {\tt subst_elemL} theorem, 72
   537   \item {\tt subst_elemL} theorem, 75
   531   \item {\tt subst_eqtyparg} theorem, 76, 88
   538   \item {\tt subst_eqtyparg} theorem, 79, 91
   532   \item {\tt subst_prodE} theorem, 74, 76
   539   \item {\tt subst_prodE} theorem, 77, 79
   533   \item {\tt subst_type} theorem, 72
   540   \item {\tt subst_type} theorem, 75
   534   \item {\tt subst_typeL} theorem, 72
   541   \item {\tt subst_typeL} theorem, 75
   535   \item {\tt Suc} constant, 21
   542   \item {\tt Suc} constant, 25
   536   \item {\tt Suc_not_Zero} theorem, 21
   543   \item {\tt Suc_not_Zero} theorem, 25
   537   \item {\tt succ} constant, 69
   544   \item {\tt succ} constant, 72
   538   \item {\tt SUM} symbol, 70, 71
   545   \item {\tt SUM} symbol, 73, 74
   539   \item {\tt Sum} constant, 69
   546   \item {\tt Sum} constant, 72
   540   \item {\tt Sum} theory, 20
   547   \item {\tt Sum} theory, 24
   541   \item {\tt sum_case} constant, 21
   548   \item {\tt sum_case} constant, 25
   542   \item {\tt sum_case_Inl} theorem, 21
   549   \item {\tt sum_case_Inl} theorem, 25
   543   \item {\tt sum_case_Inr} theorem, 21
   550   \item {\tt sum_case_Inr} theorem, 25
   544   \item {\tt SumC} theorem, 74
   551   \item {\tt SumC} theorem, 77
   545   \item {\tt SumE} theorem, 74, 79, 83
   552   \item {\tt SumE} theorem, 77, 82, 86
   546   \item {\tt sumE} theorem, 21
   553   \item {\tt sumE} theorem, 25
   547   \item {\tt SumE_fst} theorem, 74, 76, 88, 89
   554   \item {\tt SumE_fst} theorem, 77, 79, 91, 92
   548   \item {\tt SumE_snd} theorem, 74, 76, 90
   555   \item {\tt SumE_snd} theorem, 77, 79, 93
   549   \item {\tt SumEL} theorem, 74
   556   \item {\tt SumEL} theorem, 77
   550   \item {\tt SumF} theorem, 74
   557   \item {\tt SumF} theorem, 77
   551   \item {\tt SumFL} theorem, 74
   558   \item {\tt SumFL} theorem, 77
   552   \item {\tt SumI} theorem, 74, 84
   559   \item {\tt SumI} theorem, 77, 87
   553   \item {\tt SumIL} theorem, 74
   560   \item {\tt SumIL} theorem, 77
   554   \item {\tt SumIL2} theorem, 76
   561   \item {\tt SumIL2} theorem, 79
   555   \item {\tt surj} constant, 13, 17
   562   \item {\tt surj} constant, 17, 21
   556   \item {\tt surj_def} theorem, 17
   563   \item {\tt surj_def} theorem, 21
   557   \item {\tt surjective_pairing} theorem, 19
   564   \item {\tt surjective_pairing} theorem, 23
   558   \item {\tt surjective_sum} theorem, 21
   565   \item {\tt surjective_sum} theorem, 25
   559   \item {\tt swap} theorem, 8
   566   \item {\tt swap} theorem, 12
   560   \item {\tt swap_res_tac}, 53
   567   \item {\tt swap_res_tac}, 57
   561   \item {\tt sym} theorem, 7, 58
   568   \item {\tt sym} theorem, 11, 61
   562   \item {\tt sym_elem} theorem, 72
   569   \item {\tt sym_elem} theorem, 75
   563   \item {\tt sym_type} theorem, 72
   570   \item {\tt sym_type} theorem, 75
   564   \item {\tt symL} theorem, 59
   571   \item {\tt symL} theorem, 62
   565 
   572 
   566   \indexspace
   573   \indexspace
   567 
   574 
   568   \item {\tt T} constant, 69
   575   \item {\tt T} constant, 72
   569   \item {\textit {t}} type, 68
   576   \item {\textit {t}} type, 71
   570   \item {\tt take} constant, 24
   577   \item {\tt take} constant, 28
   571   \item {\tt takeWhile} constant, 24
   578   \item {\tt takeWhile} constant, 28
   572   \item {\tt TC} theorem, 75
   579   \item {\tt TC} theorem, 78
   573   \item {\tt TE} theorem, 75
   580   \item {\tt TE} theorem, 78
   574   \item {\tt TEL} theorem, 75
   581   \item {\tt TEL} theorem, 78
   575   \item {\tt term} class, 3, 55
   582   \item {\tt term} class, 7, 58
   576   \item {\tt test_assume_tac}, \bold{77}
   583   \item {\tt test_assume_tac}, \bold{80}
   577   \item {\tt TF} theorem, 75
   584   \item {\tt TF} theorem, 78
   578   \item {\tt THE} symbol, 56
   585   \item {\tt THE} symbol, 59
   579   \item {\tt The} constant, 56
   586   \item {\tt The} constant, 59
   580   \item {\tt The} theorem, 58
   587   \item {\tt The} theorem, 61
   581   \item {\tt thinL} theorem, 58
   588   \item {\tt thinL} theorem, 61
   582   \item {\tt thinR} theorem, 58
   589   \item {\tt thinR} theorem, 61
   583   \item {\tt TI} theorem, 75
   590   \item {\tt TI} theorem, 78
   584   \item {\tt times} class, 3
   591   \item {\tt times} class, 7
   585   \item {\tt tl} constant, 24
   592   \item {\tt tl} constant, 28
   586   \item tracing
   593   \item tracing
   587     \subitem of unification, 4
   594     \subitem of unification, 8
   588   \item {\tt trans} theorem, 7, 58
   595   \item {\tt trans} theorem, 11, 61
   589   \item {\tt trans_elem} theorem, 72
   596   \item {\tt trans_elem} theorem, 75
   590   \item {\tt trans_red} theorem, 72
   597   \item {\tt trans_red} theorem, 75
   591   \item {\tt trans_tac}, 23
   598   \item {\tt trans_tac}, 27
   592   \item {\tt trans_type} theorem, 72
   599   \item {\tt trans_type} theorem, 75
   593   \item {\tt True} constant, 2, 56
   600   \item {\tt True} constant, 6, 59
   594   \item {\tt True_def} theorem, 6, 58
   601   \item {\tt True_def} theorem, 10, 61
   595   \item {\tt True_or_False} theorem, 5, 6
   602   \item {\tt True_or_False} theorem, 9, 10
   596   \item {\tt TrueI} theorem, 7
   603   \item {\tt TrueI} theorem, 11
   597   \item {\tt Trueprop} constant, 2, 56
   604   \item {\tt Trueprop} constant, 6, 59
   598   \item {\tt TrueR} theorem, 59
   605   \item {\tt TrueR} theorem, 62
   599   \item {\tt tt} constant, 69
   606   \item {\tt tt} constant, 72
   600   \item {\tt Type} constant, 69
   607   \item {\tt Type} constant, 72
   601   \item type definition, \bold{26}
   608   \item type definition, \bold{30}
   602   \item {\tt typechk_tac}, \bold{77}, 82, 85, 89, 90
   609   \item {\tt typechk_tac}, \bold{80}, 85, 88, 92, 93
   603   \item {\tt typedef}, 23
   610   \item {\tt typedef}, 27
   604 
   611 
   605   \indexspace
   612   \indexspace
   606 
   613 
   607   \item {\tt UN} symbol, 10--12
   614   \item {\tt UN} symbol, 14--16
   608   \item {\tt Un} symbol, 10
   615   \item {\tt Un} symbol, 14
   609   \item {\tt Un1} theorem, 12
   616   \item {\tt Un1} theorem, 16
   610   \item {\tt Un2} theorem, 12
   617   \item {\tt Un2} theorem, 16
   611   \item {\tt Un_absorb} theorem, 16
   618   \item {\tt Un_absorb} theorem, 20
   612   \item {\tt Un_assoc} theorem, 16
   619   \item {\tt Un_assoc} theorem, 20
   613   \item {\tt Un_commute} theorem, 16
   620   \item {\tt Un_commute} theorem, 20
   614   \item {\tt Un_def} theorem, 13
   621   \item {\tt Un_def} theorem, 17
   615   \item {\tt UN_E} theorem, 15
   622   \item {\tt UN_E} theorem, 19
   616   \item {\tt UN_I} theorem, 15
   623   \item {\tt UN_I} theorem, 19
   617   \item {\tt Un_Int_distrib} theorem, 16
   624   \item {\tt Un_Int_distrib} theorem, 20
   618   \item {\tt Un_Inter} theorem, 16
   625   \item {\tt Un_Inter} theorem, 20
   619   \item {\tt Un_least} theorem, 16
   626   \item {\tt Un_least} theorem, 20
   620   \item {\tt Un_Union_image} theorem, 16
   627   \item {\tt Un_Union_image} theorem, 20
   621   \item {\tt Un_upper1} theorem, 16
   628   \item {\tt Un_upper1} theorem, 20
   622   \item {\tt Un_upper2} theorem, 16
   629   \item {\tt Un_upper2} theorem, 20
   623   \item {\tt UnCI} theorem, 12, 15
   630   \item {\tt UnCI} theorem, 16, 19
   624   \item {\tt UnE} theorem, 15
   631   \item {\tt UnE} theorem, 19
   625   \item {\tt UnI1} theorem, 15
   632   \item {\tt UnI1} theorem, 19
   626   \item {\tt UnI2} theorem, 15
   633   \item {\tt UnI2} theorem, 19
   627   \item unification
   634   \item unification
   628     \subitem incompleteness of, 4
   635     \subitem incompleteness of, 8
   629   \item {\tt Unify.trace_types}, 4
   636   \item {\tt Unify.trace_types}, 8
   630   \item {\tt UNION} constant, 10
   637   \item {\tt UNION} constant, 14
   631   \item {\tt Union} constant, 10
   638   \item {\tt Union} constant, 14
   632   \item {\tt UNION1} constant, 10
   639   \item {\tt UNION1} constant, 14
   633   \item {\tt UNION1_def} theorem, 13
   640   \item {\tt UNION1_def} theorem, 17
   634   \item {\tt UNION_def} theorem, 13
   641   \item {\tt UNION_def} theorem, 17
   635   \item {\tt Union_def} theorem, 13
   642   \item {\tt Union_def} theorem, 17
   636   \item {\tt Union_least} theorem, 16
   643   \item {\tt Union_least} theorem, 20
   637   \item {\tt Union_Un_distrib} theorem, 16
   644   \item {\tt Union_Un_distrib} theorem, 20
   638   \item {\tt Union_upper} theorem, 16
   645   \item {\tt Union_upper} theorem, 20
   639   \item {\tt UnionE} theorem, 15
   646   \item {\tt UnionE} theorem, 19
   640   \item {\tt UnionI} theorem, 15
   647   \item {\tt UnionI} theorem, 19
   641   \item {\tt unit_eq} theorem, 20
   648   \item {\tt unit_eq} theorem, 24
   642 
   649 
   643   \indexspace
   650   \indexspace
   644 
   651 
   645   \item {\tt when} constant, 69, 74, 83
   652   \item {\tt when} constant, 72, 77, 86
   646 
   653 
   647   \indexspace
   654   \indexspace
   648 
   655 
   649   \item {\tt zero_ne_succ} theorem, 72, 73
   656   \item {\tt zero_ne_succ} theorem, 75, 76
   650   \item {\tt ZF} theory, 1
   657   \item {\tt ZF} theory, 5
   651 
   658 
   652 \end{theindex}
   659 \end{theindex}