doc-src/ZF/logics-ZF.ind
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6155:e387d188d0ca 6156:0d52e7cbff29
       
     1 \begin{theindex}
       
     2 
       
     3   \item {\tt\#*} symbol, 45
       
     4   \item {\tt\#+} symbol, 45
       
     5   \item {\tt\#-} symbol, 45
       
     6   \item {\tt\&} symbol, 5
       
     7   \item {\tt *} symbol, 25
       
     8   \item {\tt +} symbol, 41
       
     9   \item {\tt -} symbol, 24
       
    10   \item {\tt -->} symbol, 5
       
    11   \item {\tt ->} symbol, 25
       
    12   \item {\tt -``} symbol, 24
       
    13   \item {\tt :} symbol, 24
       
    14   \item {\tt <->} symbol, 5
       
    15   \item {\tt <=} symbol, 24
       
    16   \item {\tt =} symbol, 5
       
    17   \item {\tt `} symbol, 24
       
    18   \item {\tt ``} symbol, 24
       
    19   \item {\tt |} symbol, 5
       
    20 
       
    21   \indexspace
       
    22 
       
    23   \item {\tt 0} constant, 24
       
    24 
       
    25   \indexspace
       
    26 
       
    27   \item {\tt add_0} theorem, 45
       
    28   \item {\tt add_mult_dist} theorem, 45
       
    29   \item {\tt add_succ} theorem, 45
       
    30   \item {\tt ALL} symbol, 5, 25
       
    31   \item {\tt All} constant, 5
       
    32   \item {\tt all_dupE} theorem, 3, 7
       
    33   \item {\tt all_impE} theorem, 7
       
    34   \item {\tt allE} theorem, 3, 7
       
    35   \item {\tt allI} theorem, 6
       
    36   \item {\tt and_def} theorem, 41
       
    37   \item {\tt apply_def} theorem, 29
       
    38   \item {\tt apply_equality} theorem, 38, 39, 69
       
    39   \item {\tt apply_equality2} theorem, 38
       
    40   \item {\tt apply_iff} theorem, 38
       
    41   \item {\tt apply_Pair} theorem, 38, 69
       
    42   \item {\tt apply_type} theorem, 38
       
    43   \item {\tt Arith} theory, 42
       
    44   \item assumptions
       
    45     \subitem contradictory, 14
       
    46 
       
    47   \indexspace
       
    48 
       
    49   \item {\tt Ball} constant, 24, 27
       
    50   \item {\tt ball_cong} theorem, 31, 32
       
    51   \item {\tt Ball_def} theorem, 28
       
    52   \item {\tt ballE} theorem, 31, 32
       
    53   \item {\tt ballI} theorem, 31
       
    54   \item {\tt beta} theorem, 38, 39
       
    55   \item {\tt Bex} constant, 24, 27
       
    56   \item {\tt bex_cong} theorem, 31, 32
       
    57   \item {\tt Bex_def} theorem, 28
       
    58   \item {\tt bexCI} theorem, 31
       
    59   \item {\tt bexE} theorem, 31
       
    60   \item {\tt bexI} theorem, 31
       
    61   \item {\tt bij} constant, 44
       
    62   \item {\tt bij_converse_bij} theorem, 44
       
    63   \item {\tt bij_def} theorem, 44
       
    64   \item {\tt bij_disjoint_Un} theorem, 44
       
    65   \item {\tt Blast_tac}, 15, 67, 68
       
    66   \item {\tt blast_tac}, 16, 17, 19
       
    67   \item {\tt bnd_mono_def} theorem, 43
       
    68   \item {\tt Bool} theory, 39
       
    69   \item {\tt bool_0I} theorem, 41
       
    70   \item {\tt bool_1I} theorem, 41
       
    71   \item {\tt bool_def} theorem, 41
       
    72   \item {\tt boolE} theorem, 41
       
    73   \item {\tt bspec} theorem, 31
       
    74 
       
    75   \indexspace
       
    76 
       
    77   \item {\tt case} constant, 41
       
    78   \item {\tt case_def} theorem, 41
       
    79   \item {\tt case_Inl} theorem, 41
       
    80   \item {\tt case_Inr} theorem, 41
       
    81   \item {\tt coinduct} theorem, 43
       
    82   \item {\tt coinductive}, 57--62
       
    83   \item {\tt Collect} constant, 24, 25, 30
       
    84   \item {\tt Collect_def} theorem, 28
       
    85   \item {\tt Collect_subset} theorem, 35
       
    86   \item {\tt CollectD1} theorem, 32, 33
       
    87   \item {\tt CollectD2} theorem, 32, 33
       
    88   \item {\tt CollectE} theorem, 32, 33
       
    89   \item {\tt CollectI} theorem, 33
       
    90   \item {\tt comp_assoc} theorem, 44
       
    91   \item {\tt comp_bij} theorem, 44
       
    92   \item {\tt comp_def} theorem, 44
       
    93   \item {\tt comp_func} theorem, 44
       
    94   \item {\tt comp_func_apply} theorem, 44
       
    95   \item {\tt comp_inj} theorem, 44
       
    96   \item {\tt comp_surj} theorem, 44
       
    97   \item {\tt comp_type} theorem, 44
       
    98   \item {\tt cond_0} theorem, 41
       
    99   \item {\tt cond_1} theorem, 41
       
   100   \item {\tt cond_def} theorem, 41
       
   101   \item congruence rules, 32
       
   102   \item {\tt conj_cong}, 4
       
   103   \item {\tt conj_impE} theorem, 7, 8
       
   104   \item {\tt conjE} theorem, 7
       
   105   \item {\tt conjI} theorem, 6
       
   106   \item {\tt conjunct1} theorem, 6
       
   107   \item {\tt conjunct2} theorem, 6
       
   108   \item {\tt cons} constant, 23, 24
       
   109   \item {\tt cons_def} theorem, 29
       
   110   \item {\tt Cons_iff} theorem, 47
       
   111   \item {\tt consCI} theorem, 34
       
   112   \item {\tt consE} theorem, 34
       
   113   \item {\tt ConsI} theorem, 47
       
   114   \item {\tt consI1} theorem, 34
       
   115   \item {\tt consI2} theorem, 34
       
   116   \item {\tt converse} constant, 24, 37
       
   117   \item {\tt converse_def} theorem, 29
       
   118   \item {\tt cut_facts_tac}, 17
       
   119 
       
   120   \indexspace
       
   121 
       
   122   \item {\tt datatype}, 48--55
       
   123   \item {\tt Diff_cancel} theorem, 40
       
   124   \item {\tt Diff_contains} theorem, 35
       
   125   \item {\tt Diff_def} theorem, 28
       
   126   \item {\tt Diff_disjoint} theorem, 40
       
   127   \item {\tt Diff_Int} theorem, 40
       
   128   \item {\tt Diff_partition} theorem, 40
       
   129   \item {\tt Diff_subset} theorem, 35
       
   130   \item {\tt Diff_Un} theorem, 40
       
   131   \item {\tt DiffD1} theorem, 34
       
   132   \item {\tt DiffD2} theorem, 34
       
   133   \item {\tt DiffE} theorem, 34
       
   134   \item {\tt DiffI} theorem, 34
       
   135   \item {\tt disj_impE} theorem, 7, 8, 12
       
   136   \item {\tt disjCI} theorem, 9
       
   137   \item {\tt disjE} theorem, 6
       
   138   \item {\tt disjI1} theorem, 6
       
   139   \item {\tt disjI2} theorem, 6
       
   140   \item {\tt div} symbol, 45
       
   141   \item {\tt div_def} theorem, 45
       
   142   \item {\tt domain} constant, 24, 37
       
   143   \item {\tt domain_def} theorem, 29
       
   144   \item {\tt domain_of_fun} theorem, 38
       
   145   \item {\tt domain_subset} theorem, 37
       
   146   \item {\tt domain_type} theorem, 38
       
   147   \item {\tt domainE} theorem, 37
       
   148   \item {\tt domainI} theorem, 37
       
   149   \item {\tt double_complement} theorem, 40
       
   150   \item {\tt dresolve_tac}, 66
       
   151 
       
   152   \indexspace
       
   153 
       
   154   \item {\tt empty_subsetI} theorem, 31
       
   155   \item {\tt emptyE} theorem, 31
       
   156   \item {\tt eq_mp_tac}, \bold{8}
       
   157   \item {\tt equalityD1} theorem, 31
       
   158   \item {\tt equalityD2} theorem, 31
       
   159   \item {\tt equalityE} theorem, 31
       
   160   \item {\tt equalityI} theorem, 31, 65
       
   161   \item {\tt equals0D} theorem, 31
       
   162   \item {\tt equals0I} theorem, 31
       
   163   \item {\tt eresolve_tac}, 14
       
   164   \item {\tt eta} theorem, 38, 39
       
   165   \item {\tt EX} symbol, 5, 25
       
   166   \item {\tt Ex} constant, 5
       
   167   \item {\tt EX!} symbol, 5
       
   168   \item {\tt ex/Term} theory, 49
       
   169   \item {\tt Ex1} constant, 5
       
   170   \item {\tt ex1_def} theorem, 6
       
   171   \item {\tt ex1E} theorem, 7
       
   172   \item {\tt ex1I} theorem, 7
       
   173   \item {\tt ex_impE} theorem, 7
       
   174   \item {\tt exCI} theorem, 9, 13
       
   175   \item {\tt excluded_middle} theorem, 9
       
   176   \item {\tt exE} theorem, 6
       
   177   \item {\tt exhaust_tac}, \bold{51}
       
   178   \item {\tt exI} theorem, 6
       
   179   \item {\tt extension} theorem, 28
       
   180 
       
   181   \indexspace
       
   182 
       
   183   \item {\tt False} constant, 5
       
   184   \item {\tt FalseE} theorem, 6
       
   185   \item {\tt field} constant, 24
       
   186   \item {\tt field_def} theorem, 29
       
   187   \item {\tt field_subset} theorem, 37
       
   188   \item {\tt fieldCI} theorem, 37
       
   189   \item {\tt fieldE} theorem, 37
       
   190   \item {\tt fieldI1} theorem, 37
       
   191   \item {\tt fieldI2} theorem, 37
       
   192   \item {\tt Fin.consI} theorem, 46
       
   193   \item {\tt Fin.emptyI} theorem, 46
       
   194   \item {\tt Fin_induct} theorem, 46
       
   195   \item {\tt Fin_mono} theorem, 46
       
   196   \item {\tt Fin_subset} theorem, 46
       
   197   \item {\tt Fin_UnI} theorem, 46
       
   198   \item {\tt Fin_UnionI} theorem, 46
       
   199   \item first-order logic, 3--21
       
   200   \item {\tt Fixedpt} theory, 42
       
   201   \item {\tt flat} constant, 47
       
   202   \item {\tt FOL} theory, 3, 9
       
   203   \item {\tt FOL_cs}, \bold{9}, 48
       
   204   \item {\tt FOL_ss}, \bold{4}, 46
       
   205   \item {\tt foundation} theorem, 28
       
   206   \item {\tt fst} constant, 24, 30
       
   207   \item {\tt fst_conv} theorem, 36
       
   208   \item {\tt fst_def} theorem, 29
       
   209   \item {\tt fun_disjoint_apply1} theorem, 38, 69
       
   210   \item {\tt fun_disjoint_apply2} theorem, 38
       
   211   \item {\tt fun_disjoint_Un} theorem, 38, 70
       
   212   \item {\tt fun_empty} theorem, 38
       
   213   \item {\tt fun_extension} theorem, 38, 39
       
   214   \item {\tt fun_is_rel} theorem, 38
       
   215   \item {\tt fun_single} theorem, 38
       
   216   \item function applications
       
   217     \subitem in \ZF, 24
       
   218 
       
   219   \indexspace
       
   220 
       
   221   \item {\tt gfp_def} theorem, 43
       
   222   \item {\tt gfp_least} theorem, 43
       
   223   \item {\tt gfp_mono} theorem, 43
       
   224   \item {\tt gfp_subset} theorem, 43
       
   225   \item {\tt gfp_Tarski} theorem, 43
       
   226   \item {\tt gfp_upperbound} theorem, 43
       
   227   \item {\tt Goalw}, 16, 17
       
   228 
       
   229   \indexspace
       
   230 
       
   231   \item {\tt hyp_subst_tac}, 4
       
   232 
       
   233   \indexspace
       
   234 
       
   235   \item {\textit {i}} type, 23
       
   236   \item {\tt id} constant, 44
       
   237   \item {\tt id_def} theorem, 44
       
   238   \item {\tt if} constant, 24
       
   239   \item {\tt if_def} theorem, 16, 28
       
   240   \item {\tt if_not_P} theorem, 34
       
   241   \item {\tt if_P} theorem, 34
       
   242   \item {\tt ifE} theorem, 17
       
   243   \item {\tt iff_def} theorem, 6
       
   244   \item {\tt iff_impE} theorem, 7
       
   245   \item {\tt iffCE} theorem, 9
       
   246   \item {\tt iffD1} theorem, 7
       
   247   \item {\tt iffD2} theorem, 7
       
   248   \item {\tt iffE} theorem, 7
       
   249   \item {\tt iffI} theorem, 7, 17
       
   250   \item {\tt ifI} theorem, 17
       
   251   \item {\tt IFOL} theory, 3
       
   252   \item {\tt IFOL_ss}, \bold{4}
       
   253   \item {\tt image_def} theorem, 29
       
   254   \item {\tt imageE} theorem, 37
       
   255   \item {\tt imageI} theorem, 37
       
   256   \item {\tt imp_impE} theorem, 7, 12
       
   257   \item {\tt impCE} theorem, 9
       
   258   \item {\tt impE} theorem, 7, 8
       
   259   \item {\tt impI} theorem, 6
       
   260   \item {\tt in} symbol, 26
       
   261   \item {\tt induct} theorem, 43
       
   262   \item {\tt induct_tac}, \bold{51}
       
   263   \item {\tt inductive}, 57--62
       
   264   \item {\tt Inf} constant, 24, 30
       
   265   \item {\tt infinity} theorem, 29
       
   266   \item {\tt inj} constant, 44
       
   267   \item {\tt inj_converse_inj} theorem, 44
       
   268   \item {\tt inj_def} theorem, 44
       
   269   \item {\tt Inl} constant, 41
       
   270   \item {\tt Inl_def} theorem, 41
       
   271   \item {\tt Inl_inject} theorem, 41
       
   272   \item {\tt Inl_neq_Inr} theorem, 41
       
   273   \item {\tt Inr} constant, 41
       
   274   \item {\tt Inr_def} theorem, 41
       
   275   \item {\tt Inr_inject} theorem, 41
       
   276   \item {\tt INT} symbol, 25, 27
       
   277   \item {\tt Int} symbol, 24
       
   278   \item {\tt Int_absorb} theorem, 40
       
   279   \item {\tt Int_assoc} theorem, 40
       
   280   \item {\tt Int_commute} theorem, 40
       
   281   \item {\tt Int_def} theorem, 28
       
   282   \item {\tt INT_E} theorem, 33
       
   283   \item {\tt Int_greatest} theorem, 35, 65, 66
       
   284   \item {\tt INT_I} theorem, 33
       
   285   \item {\tt Int_lower1} theorem, 35, 65
       
   286   \item {\tt Int_lower2} theorem, 35, 65
       
   287   \item {\tt Int_Un_distrib} theorem, 40
       
   288   \item {\tt Int_Union_RepFun} theorem, 40
       
   289   \item {\tt IntD1} theorem, 34
       
   290   \item {\tt IntD2} theorem, 34
       
   291   \item {\tt IntE} theorem, 34, 66
       
   292   \item {\tt Inter} constant, 24
       
   293   \item {\tt Inter_def} theorem, 28
       
   294   \item {\tt Inter_greatest} theorem, 35
       
   295   \item {\tt Inter_lower} theorem, 35
       
   296   \item {\tt Inter_Un_distrib} theorem, 40
       
   297   \item {\tt InterD} theorem, 33
       
   298   \item {\tt InterE} theorem, 33
       
   299   \item {\tt InterI} theorem, 32, 33
       
   300   \item {\tt IntI} theorem, 34
       
   301   \item {\tt IntPr.best_tac}, \bold{9}
       
   302   \item {\tt IntPr.fast_tac}, \bold{8}, 11
       
   303   \item {\tt IntPr.inst_step_tac}, \bold{8}
       
   304   \item {\tt IntPr.safe_step_tac}, \bold{8}
       
   305   \item {\tt IntPr.safe_tac}, \bold{8}
       
   306   \item {\tt IntPr.step_tac}, \bold{8}
       
   307 
       
   308   \indexspace
       
   309 
       
   310   \item {\tt lam} symbol, 25, 27
       
   311   \item {\tt lam_def} theorem, 29
       
   312   \item {\tt lam_type} theorem, 38
       
   313   \item {\tt Lambda} constant, 24, 27
       
   314   \item $\lambda$-abstractions
       
   315     \subitem in \ZF, 25
       
   316   \item {\tt lamE} theorem, 38, 39
       
   317   \item {\tt lamI} theorem, 38, 39
       
   318   \item {\tt le_cs}, \bold{48}
       
   319   \item {\tt left_comp_id} theorem, 44
       
   320   \item {\tt left_comp_inverse} theorem, 44
       
   321   \item {\tt left_inverse} theorem, 44
       
   322   \item {\tt length} constant, 47
       
   323   \item {\tt Let} constant, 23, 24
       
   324   \item {\tt let} symbol, 26
       
   325   \item {\tt Let_def} theorem, 23, 28
       
   326   \item {\tt lfp_def} theorem, 43
       
   327   \item {\tt lfp_greatest} theorem, 43
       
   328   \item {\tt lfp_lowerbound} theorem, 43
       
   329   \item {\tt lfp_mono} theorem, 43
       
   330   \item {\tt lfp_subset} theorem, 43
       
   331   \item {\tt lfp_Tarski} theorem, 43
       
   332   \item {\tt list} constant, 47
       
   333   \item {\tt List.induct} theorem, 47
       
   334   \item {\tt list_case} constant, 47
       
   335   \item {\tt list_mono} theorem, 47
       
   336   \item {\tt logic} class, 3
       
   337 
       
   338   \indexspace
       
   339 
       
   340   \item {\tt map} constant, 47
       
   341   \item {\tt map_app_distrib} theorem, 47
       
   342   \item {\tt map_compose} theorem, 47
       
   343   \item {\tt map_flat} theorem, 47
       
   344   \item {\tt map_ident} theorem, 47
       
   345   \item {\tt map_type} theorem, 47
       
   346   \item {\tt mem_asym} theorem, 34, 35
       
   347   \item {\tt mem_irrefl} theorem, 34
       
   348   \item {\tt mk_cases}, 54, 61
       
   349   \item {\tt mod} symbol, 45
       
   350   \item {\tt mod_def} theorem, 45
       
   351   \item {\tt mod_quo_equality} theorem, 45
       
   352   \item {\tt mp} theorem, 6
       
   353   \item {\tt mp_tac}, \bold{8}
       
   354   \item {\tt mult_0} theorem, 45
       
   355   \item {\tt mult_assoc} theorem, 45
       
   356   \item {\tt mult_commute} theorem, 45
       
   357   \item {\tt mult_succ} theorem, 45
       
   358   \item {\tt mult_type} theorem, 45
       
   359 
       
   360   \indexspace
       
   361 
       
   362   \item {\tt Nat} theory, 42
       
   363   \item {\tt nat} constant, 45
       
   364   \item {\tt nat_0I} theorem, 45
       
   365   \item {\tt nat_case} constant, 45
       
   366   \item {\tt nat_case_0} theorem, 45
       
   367   \item {\tt nat_case_def} theorem, 45
       
   368   \item {\tt nat_case_succ} theorem, 45
       
   369   \item {\tt nat_def} theorem, 45
       
   370   \item {\tt nat_induct} theorem, 45
       
   371   \item {\tt nat_succI} theorem, 45
       
   372   \item {\tt Nil_Cons_iff} theorem, 47
       
   373   \item {\tt NilI} theorem, 47
       
   374   \item {\tt Not} constant, 5
       
   375   \item {\tt not_def} theorem, 6, 41
       
   376   \item {\tt not_impE} theorem, 7
       
   377   \item {\tt notE} theorem, 7, 8
       
   378   \item {\tt notI} theorem, 7
       
   379   \item {\tt notnotD} theorem, 9
       
   380 
       
   381   \indexspace
       
   382 
       
   383   \item {\tt O} symbol, 44
       
   384   \item {\textit {o}} type, 3
       
   385   \item {\tt or_def} theorem, 41
       
   386 
       
   387   \indexspace
       
   388 
       
   389   \item {\tt Pair} constant, 24, 25
       
   390   \item {\tt Pair_def} theorem, 29
       
   391   \item {\tt Pair_inject} theorem, 36
       
   392   \item {\tt Pair_inject1} theorem, 36
       
   393   \item {\tt Pair_inject2} theorem, 36
       
   394   \item {\tt Pair_neq_0} theorem, 36
       
   395   \item {\tt pairing} theorem, 33
       
   396   \item {\tt Perm} theory, 42
       
   397   \item {\tt Pi} constant, 24, 27, 39
       
   398   \item {\tt Pi_def} theorem, 29
       
   399   \item {\tt Pi_type} theorem, 38, 39
       
   400   \item {\tt Pow} constant, 24
       
   401   \item {\tt Pow_iff} theorem, 28
       
   402   \item {\tt Pow_mono} theorem, 65
       
   403   \item {\tt PowD} theorem, 31, 66
       
   404   \item {\tt PowI} theorem, 31, 66
       
   405   \item {\tt primrec}, 55--57
       
   406   \item {\tt PrimReplace} constant, 24, 30
       
   407   \item priorities, 1
       
   408   \item {\tt PROD} symbol, 25, 27
       
   409   \item {\tt prop_cs}, \bold{9}
       
   410 
       
   411   \indexspace
       
   412 
       
   413   \item {\tt qcase_def} theorem, 42
       
   414   \item {\tt qconverse} constant, 39
       
   415   \item {\tt qconverse_def} theorem, 42
       
   416   \item {\tt qed_spec_mp}, 54
       
   417   \item {\tt qfsplit_def} theorem, 42
       
   418   \item {\tt QInl_def} theorem, 42
       
   419   \item {\tt QInr_def} theorem, 42
       
   420   \item {\tt QPair} theory, 39
       
   421   \item {\tt QPair_def} theorem, 42
       
   422   \item {\tt QSigma} constant, 39
       
   423   \item {\tt QSigma_def} theorem, 42
       
   424   \item {\tt qsplit} constant, 39
       
   425   \item {\tt qsplit_def} theorem, 42
       
   426   \item {\tt qsum_def} theorem, 42
       
   427   \item {\tt QUniv} theory, 46
       
   428 
       
   429   \indexspace
       
   430 
       
   431   \item {\tt range} constant, 24
       
   432   \item {\tt range_def} theorem, 29
       
   433   \item {\tt range_of_fun} theorem, 38, 39
       
   434   \item {\tt range_subset} theorem, 37
       
   435   \item {\tt range_type} theorem, 38
       
   436   \item {\tt rangeE} theorem, 37
       
   437   \item {\tt rangeI} theorem, 37
       
   438   \item {\tt rank} constant, 62
       
   439   \item recursion
       
   440     \subitem primitive, 57
       
   441   \item recursive functions, \see{recursion}{55}
       
   442   \item {\tt refl} theorem, 6
       
   443   \item {\tt RepFun} constant, 24, 27, 30, 32
       
   444   \item {\tt RepFun_def} theorem, 28
       
   445   \item {\tt RepFunE} theorem, 33
       
   446   \item {\tt RepFunI} theorem, 33
       
   447   \item {\tt Replace} constant, 24, 25, 30, 32
       
   448   \item {\tt Replace_def} theorem, 28
       
   449   \item {\tt ReplaceE} theorem, 33
       
   450   \item {\tt ReplaceI} theorem, 33
       
   451   \item {\tt replacement} theorem, 28
       
   452   \item {\tt restrict} constant, 24, 30
       
   453   \item {\tt restrict} theorem, 38
       
   454   \item {\tt restrict_bij} theorem, 44
       
   455   \item {\tt restrict_def} theorem, 29
       
   456   \item {\tt restrict_type} theorem, 38
       
   457   \item {\tt rev} constant, 47
       
   458   \item {\tt rew_tac}, 17
       
   459   \item {\tt rewrite_rule}, 17
       
   460   \item {\tt right_comp_id} theorem, 44
       
   461   \item {\tt right_comp_inverse} theorem, 44
       
   462   \item {\tt right_inverse} theorem, 44
       
   463 
       
   464   \indexspace
       
   465 
       
   466   \item {\tt separation} theorem, 33
       
   467   \item set theory, 22--70
       
   468   \item {\tt Sigma} constant, 24, 27, 30, 36
       
   469   \item {\tt Sigma_def} theorem, 29
       
   470   \item {\tt SigmaE} theorem, 36
       
   471   \item {\tt SigmaE2} theorem, 36
       
   472   \item {\tt SigmaI} theorem, 36
       
   473   \item simplification
       
   474     \subitem of conjunctions, 4
       
   475   \item {\tt singletonE} theorem, 34
       
   476   \item {\tt singletonI} theorem, 34
       
   477   \item {\tt snd} constant, 24, 30
       
   478   \item {\tt snd_conv} theorem, 36
       
   479   \item {\tt snd_def} theorem, 29
       
   480   \item {\tt spec} theorem, 6
       
   481   \item {\tt split} constant, 24, 30
       
   482   \item {\tt split} theorem, 36
       
   483   \item {\tt split_def} theorem, 29
       
   484   \item {\tt ssubst} theorem, 7
       
   485   \item {\tt Step_tac}, 20
       
   486   \item {\tt step_tac}, 21
       
   487   \item {\tt subset_def} theorem, 28
       
   488   \item {\tt subset_refl} theorem, 31
       
   489   \item {\tt subset_trans} theorem, 31
       
   490   \item {\tt subsetCE} theorem, 31
       
   491   \item {\tt subsetD} theorem, 31, 68
       
   492   \item {\tt subsetI} theorem, 31, 66, 67
       
   493   \item {\tt subst} theorem, 6
       
   494   \item {\tt succ} constant, 24, 30
       
   495   \item {\tt succ_def} theorem, 29
       
   496   \item {\tt succ_inject} theorem, 34
       
   497   \item {\tt succ_neq_0} theorem, 34
       
   498   \item {\tt succCI} theorem, 34
       
   499   \item {\tt succE} theorem, 34
       
   500   \item {\tt succI1} theorem, 34
       
   501   \item {\tt succI2} theorem, 34
       
   502   \item {\tt SUM} symbol, 25, 27
       
   503   \item {\tt Sum} theory, 39
       
   504   \item {\tt sum_def} theorem, 41
       
   505   \item {\tt sum_InlI} theorem, 41
       
   506   \item {\tt sum_InrI} theorem, 41
       
   507   \item {\tt SUM_Int_distrib1} theorem, 40
       
   508   \item {\tt SUM_Int_distrib2} theorem, 40
       
   509   \item {\tt SUM_Un_distrib1} theorem, 40
       
   510   \item {\tt SUM_Un_distrib2} theorem, 40
       
   511   \item {\tt sumE2} theorem, 41
       
   512   \item {\tt surj} constant, 44
       
   513   \item {\tt surj_def} theorem, 44
       
   514   \item {\tt swap} theorem, 9
       
   515   \item {\tt swap_res_tac}, 14
       
   516   \item {\tt sym} theorem, 7
       
   517 
       
   518   \indexspace
       
   519 
       
   520   \item {\tt term} class, 3
       
   521   \item {\tt THE} symbol, 25, 27, 35
       
   522   \item {\tt The} constant, 24, 27, 30
       
   523   \item {\tt the_def} theorem, 28
       
   524   \item {\tt the_equality} theorem, 34, 35
       
   525   \item {\tt theI} theorem, 34, 35
       
   526   \item {\tt trace_induct}, \bold{59}
       
   527   \item {\tt trans} theorem, 7
       
   528   \item {\tt True} constant, 5
       
   529   \item {\tt True_def} theorem, 6
       
   530   \item {\tt TrueI} theorem, 7
       
   531   \item {\tt Trueprop} constant, 5
       
   532 
       
   533   \indexspace
       
   534 
       
   535   \item {\tt UN} symbol, 25, 27
       
   536   \item {\tt Un} symbol, 24
       
   537   \item {\tt Un_absorb} theorem, 40
       
   538   \item {\tt Un_assoc} theorem, 40
       
   539   \item {\tt Un_commute} theorem, 40
       
   540   \item {\tt Un_def} theorem, 28
       
   541   \item {\tt UN_E} theorem, 33
       
   542   \item {\tt UN_I} theorem, 33
       
   543   \item {\tt Un_Int_distrib} theorem, 40
       
   544   \item {\tt Un_Inter_RepFun} theorem, 40
       
   545   \item {\tt Un_least} theorem, 35
       
   546   \item {\tt Un_upper1} theorem, 35
       
   547   \item {\tt Un_upper2} theorem, 35
       
   548   \item {\tt UnCI} theorem, 32, 34
       
   549   \item {\tt UnE} theorem, 34
       
   550   \item {\tt UnI1} theorem, 32, 34, 69
       
   551   \item {\tt UnI2} theorem, 32, 34
       
   552   \item {\tt Union} constant, 24
       
   553   \item {\tt Union_iff} theorem, 28
       
   554   \item {\tt Union_least} theorem, 35
       
   555   \item {\tt Union_Un_distrib} theorem, 40
       
   556   \item {\tt Union_upper} theorem, 35
       
   557   \item {\tt UnionE} theorem, 33, 67
       
   558   \item {\tt UnionI} theorem, 33, 67
       
   559   \item {\tt Univ} theory, 42
       
   560   \item {\tt Upair} constant, 23, 24, 30
       
   561   \item {\tt Upair_def} theorem, 28
       
   562   \item {\tt UpairE} theorem, 33
       
   563   \item {\tt UpairI1} theorem, 33
       
   564   \item {\tt UpairI2} theorem, 33
       
   565 
       
   566   \indexspace
       
   567 
       
   568   \item {\tt vimage_def} theorem, 29
       
   569   \item {\tt vimageE} theorem, 37
       
   570   \item {\tt vimageI} theorem, 37
       
   571 
       
   572   \indexspace
       
   573 
       
   574   \item {\tt xor_def} theorem, 41
       
   575 
       
   576   \indexspace
       
   577 
       
   578   \item {\tt ZF} theory, 22
       
   579   \item {\tt ZF_cs}, \bold{48}
       
   580   \item {\tt ZF_ss}, \bold{46}
       
   581 
       
   582 \end{theindex}