\begin{theindex}
\item {\tt !} symbol, 60, 62, 69, 70
\item {\tt[]} symbol, 82
\item {\tt\#} symbol, 82
\item {\tt\#*} symbol, 47, 128
\item {\tt\#+} symbol, 47, 128
\item {\tt\#-} symbol, 47
\item {\tt\&} symbol, 7, 60, 105
\item {\tt *} symbol, 26, 61, 79, 119
\item {\tt *} type, 76
\item {\tt +} symbol, 43, 61, 79, 119
\item {\tt +} type, 76
\item {\tt -} symbol, 25, 61, 79, 128
\item {\tt -->} symbol, 7, 60, 105, 119
\item {\tt ->} symbol, 26
\item {\tt -``} symbol, 25
\item {\tt :} symbol, 25, 68
\item {\tt <} constant, 80
\item {\tt <} symbol, 79
\item {\tt <->} symbol, 7, 105
\item {\tt <=} constant, 80
\item {\tt <=} symbol, 25, 68
\item {\tt =} symbol, 7, 60, 105, 119
\item {\tt ?} symbol, 60, 62, 69, 70
\item {\tt ?!} symbol, 60
\item {\tt\at} symbol, 60, 82
\item {\tt `} symbol, 25, 119
\item {\tt ``} symbol, 25, 68
\item \verb'{}' symbol, 68
\item {\tt |} symbol, 7, 60, 105
\item {\tt |-|} symbol, 128
\indexspace
\item {\tt 0} constant, 25, 79, 117
\indexspace
\item {\tt absdiff_def} theorem, 128
\item {\tt add_assoc} theorem, 128
\item {\tt add_commute} theorem, 128
\item {\tt add_def} theorem, 47, 128
\item {\tt add_inverse_diff} theorem, 128
\item {\tt add_mp_tac}, \bold{126}
\item {\tt add_mult_dist} theorem, 47, 128
\item {\tt add_safes}, \bold{111}
\item {\tt add_typing} theorem, 128
\item {\tt add_unsafes}, \bold{111}
\item {\tt addC0} theorem, 128
\item {\tt addC_succ} theorem, 128
\item {\tt addsplits}, \bold{76}, 81
\item {\tt ALL} symbol, 7, 26, 60, 62, 69, 70, 105
\item {\tt All} constant, 7, 60, 105
\item {\tt All_def} theorem, 64
\item {\tt all_dupE} theorem, 5, 9, 66
\item {\tt all_impE} theorem, 9
\item {\tt allE} theorem, 5, 9, 66
\item {\tt allI} theorem, 8, 66
\item {\tt allL} theorem, 107, 110
\item {\tt allL_thin} theorem, 108
\item {\tt allR} theorem, 107
\item {\tt and_def} theorem, 42, 64
\item {\tt app_def} theorem, 49
\item {\tt apply_def} theorem, 31
\item {\tt apply_equality} theorem, 39, 40, 57
\item {\tt apply_equality2} theorem, 39
\item {\tt apply_iff} theorem, 39
\item {\tt apply_Pair} theorem, 39, 57
\item {\tt apply_type} theorem, 39
\item {\tt arg_cong} theorem, 65
\item {\tt Arith} theory, 46, 80, 127
\item assumptions
\subitem contradictory, 16
\subitem in {\CTT}, 116, 126
\indexspace
\item {\tt Ball} constant, 25, 29, 68, 70
\item {\tt ball_cong} theorem, 32, 33
\item {\tt Ball_def} theorem, 30, 71
\item {\tt ballE} theorem, 32, 33, 72
\item {\tt ballI} theorem, 33, 72
\item {\tt basic} theorem, 107
\item {\tt basic_defs}, \bold{124}
\item {\tt best_tac}, \bold{112}
\item {\tt beta} theorem, 39, 40
\item {\tt Bex} constant, 25, 29, 68, 70
\item {\tt bex_cong} theorem, 32, 33
\item {\tt Bex_def} theorem, 30, 71
\item {\tt bexCI} theorem, 33, 70, 72
\item {\tt bexE} theorem, 33, 72
\item {\tt bexI} theorem, 33, 70, 72
\item {\tt bij} constant, 45
\item {\tt bij_converse_bij} theorem, 45
\item {\tt bij_def} theorem, 45
\item {\tt bij_disjoint_Un} theorem, 45
\item {\tt Blast_tac}, 54--56
\item {\tt blast_tac}, 18, 20, 21
\item {\tt bnd_mono_def} theorem, 44
\item {\tt Bool} theory, 40
\item {\textit {bool}} type, 61
\item {\tt bool_0I} theorem, 42
\item {\tt bool_1I} theorem, 42
\item {\tt bool_def} theorem, 42
\item {\tt boolE} theorem, 42
\item {\tt box_equals} theorem, 65, 67
\item {\tt bspec} theorem, 33, 72
\item {\tt butlast} constant, 82
\indexspace
\item {\tt case} constant, 43
\item {\tt case} symbol, 63, 80, 81, 87
\item {\tt case_def} theorem, 43
\item {\tt case_Inl} theorem, 43
\item {\tt case_Inr} theorem, 43
\item {\tt case_tac}, \bold{67}
\item {\tt CCL} theory, 1
\item {\tt ccontr} theorem, 66
\item {\tt classical} theorem, 66
\item {\tt coinduct} theorem, 44
\item {\tt coinductive}, 96--99
\item {\tt Collect} constant, 25, 26, 29, 68, 70
\item {\tt Collect_def} theorem, 30
\item {\tt Collect_mem_eq} theorem, 70, 71
\item {\tt Collect_subset} theorem, 36
\item {\tt CollectD} theorem, 72, 102
\item {\tt CollectD1} theorem, 32, 34
\item {\tt CollectD2} theorem, 32, 34
\item {\tt CollectE} theorem, 32, 34, 72
\item {\tt CollectI} theorem, 34, 72, 102
\item {\tt comp_assoc} theorem, 45
\item {\tt comp_bij} theorem, 45
\item {\tt comp_def} theorem, 45
\item {\tt comp_func} theorem, 45
\item {\tt comp_func_apply} theorem, 45
\item {\tt comp_inj} theorem, 45
\item {\tt comp_rls}, \bold{124}
\item {\tt comp_surj} theorem, 45
\item {\tt comp_type} theorem, 45
\item {\tt Compl} constant, 68
\item {\tt Compl_def} theorem, 71
\item {\tt Compl_disjoint} theorem, 74
\item {\tt Compl_Int} theorem, 74
\item {\tt Compl_partition} theorem, 74
\item {\tt Compl_Un} theorem, 74
\item {\tt ComplD} theorem, 73
\item {\tt ComplI} theorem, 73
\item {\tt concat} constant, 82
\item {\tt cond_0} theorem, 42
\item {\tt cond_1} theorem, 42
\item {\tt cond_def} theorem, 42
\item {\tt cong} theorem, 65
\item congruence rules, 32
\item {\tt conj_cong}, 6, 75
\item {\tt conj_impE} theorem, 9, 10
\item {\tt conjE} theorem, 9, 65
\item {\tt conjI} theorem, 8, 65
\item {\tt conjL} theorem, 107
\item {\tt conjR} theorem, 107
\item {\tt conjunct1} theorem, 8, 65
\item {\tt conjunct2} theorem, 8, 65
\item {\tt conL} theorem, 108
\item {\tt conR} theorem, 108
\item {\tt cons} constant, 25, 26
\item {\tt cons_def} theorem, 31
\item {\tt Cons_iff} theorem, 49
\item {\tt consCI} theorem, 35
\item {\tt consE} theorem, 35
\item {\tt ConsI} theorem, 49
\item {\tt consI1} theorem, 35
\item {\tt consI2} theorem, 35
\item Constructive Type Theory, 116--138
\item {\tt contr} constant, 117
\item {\tt converse} constant, 25, 39
\item {\tt converse_def} theorem, 31
\item {\tt could_res}, \bold{109}
\item {\tt could_resolve_seq}, \bold{110}
\item {\tt CTT} theory, 1, 116
\item {\tt Cube} theory, 1
\item {\tt cut} theorem, 107
\item {\tt cut_facts_tac}, 18, 19, 56
\item {\tt cutL_tac}, \bold{109}
\item {\tt cutR_tac}, \bold{109}
\indexspace
\item {\tt datatype}, 86--91
\item {\tt deepen_tac}, 16
\item {\tt diff_0_eq_0} theorem, 128
\item {\tt Diff_cancel} theorem, 41
\item {\tt Diff_contains} theorem, 36
\item {\tt Diff_def} theorem, 30
\item {\tt diff_def} theorem, 47, 128
\item {\tt Diff_disjoint} theorem, 41
\item {\tt Diff_Int} theorem, 41
\item {\tt Diff_partition} theorem, 41
\item {\tt diff_self_eq_0} theorem, 128
\item {\tt Diff_subset} theorem, 36
\item {\tt diff_succ_succ} theorem, 128
\item {\tt diff_typing} theorem, 128
\item {\tt Diff_Un} theorem, 41
\item {\tt diffC0} theorem, 128
\item {\tt DiffD1} theorem, 35
\item {\tt DiffD2} theorem, 35
\item {\tt DiffE} theorem, 35
\item {\tt DiffI} theorem, 35
\item {\tt disj_impE} theorem, 9, 10, 14
\item {\tt disjCI} theorem, 11, 66
\item {\tt disjE} theorem, 8, 65
\item {\tt disjI1} theorem, 8, 65
\item {\tt disjI2} theorem, 8, 65
\item {\tt disjL} theorem, 107
\item {\tt disjR} theorem, 107
\item {\tt div} symbol, 47, 79, 128
\item {\tt div_def} theorem, 47, 128
\item {\tt div_geq} theorem, 80
\item {\tt div_less} theorem, 80
\item {\tt Divides} theory, 80
\item {\tt domain} constant, 25, 39
\item {\tt domain_def} theorem, 31
\item {\tt domain_of_fun} theorem, 39
\item {\tt domain_subset} theorem, 38
\item {\tt domain_type} theorem, 39
\item {\tt domainE} theorem, 38, 39
\item {\tt domainI} theorem, 38, 39
\item {\tt double_complement} theorem, 41, 74
\item {\tt dresolve_tac}, 53
\item {\tt drop} constant, 82
\item {\tt dropWhile} constant, 82
\indexspace
\item {\tt Elem} constant, 117
\item {\tt elim_rls}, \bold{124}
\item {\tt elimL_rls}, \bold{124}
\item {\tt empty_def} theorem, 71
\item {\tt empty_pack}, \bold{110}
\item {\tt empty_subsetI} theorem, 33
\item {\tt emptyE} theorem, 33, 73
\item {\tt Eps} constant, 60, 62
\item {\tt Eq} constant, 117
\item {\tt eq} constant, 117, 122
\item {\tt eq_mp_tac}, \bold{10}
\item {\tt EqC} theorem, 123
\item {\tt EqE} theorem, 123
\item {\tt Eqelem} constant, 117
\item {\tt EqF} theorem, 123
\item {\tt EqFL} theorem, 123
\item {\tt EqI} theorem, 123
\item {\tt Eqtype} constant, 117
\item {\tt equal_tac}, \bold{125}
\item {\tt equal_types} theorem, 120
\item {\tt equal_typesL} theorem, 120
\item {\tt equalityCE} theorem, 70, 72, 102
\item {\tt equalityD1} theorem, 33, 72
\item {\tt equalityD2} theorem, 33, 72
\item {\tt equalityE} theorem, 33, 72
\item {\tt equalityI} theorem, 33, 52, 72
\item {\tt equals0D} theorem, 33
\item {\tt equals0I} theorem, 33
\item {\tt eresolve_tac}, 16
\item {\tt eta} theorem, 39, 40
\item {\tt EX} symbol, 7, 26, 60, 62, 69, 70, 105
\item {\tt Ex} constant, 7, 60, 105
\item {\tt EX!} symbol, 7, 60
\item {\tt Ex1} constant, 7, 60
\item {\tt Ex1_def} theorem, 64
\item {\tt ex1_def} theorem, 8
\item {\tt ex1E} theorem, 9, 66
\item {\tt ex1I} theorem, 9, 66
\item {\tt Ex_def} theorem, 64
\item {\tt ex_impE} theorem, 9
\item {\tt exCI} theorem, 11, 15, 66
\item {\tt excluded_middle} theorem, 11, 66
\item {\tt exE} theorem, 8, 66
\item {\tt exhaust_tac}, \bold{89}
\item {\tt exI} theorem, 8, 66
\item {\tt exL} theorem, 107
\item {\tt Exp} theory, 100
\item {\tt expand_if} theorem, 66, 76
\item {\tt expand_list_case} theorem, 81
\item {\tt expand_split} theorem, 77
\item {\tt expand_sum_case} theorem, 79
\item {\tt exR} theorem, 107, 110, 112
\item {\tt exR_thin} theorem, 108, 112, 113
\item {\tt ext} theorem, 63, 64
\item {\tt extension} theorem, 30
\indexspace
\item {\tt F} constant, 117
\item {\tt False} constant, 7, 60, 105
\item {\tt False_def} theorem, 64
\item {\tt FalseE} theorem, 8, 65
\item {\tt FalseL} theorem, 107
\item {\tt fast_tac}, \bold{112}
\item {\tt FE} theorem, 123, 127
\item {\tt FEL} theorem, 123
\item {\tt FF} theorem, 123
\item {\tt field} constant, 25
\item {\tt field_def} theorem, 31
\item {\tt field_subset} theorem, 38
\item {\tt fieldCI} theorem, 38
\item {\tt fieldE} theorem, 38
\item {\tt fieldI1} theorem, 38
\item {\tt fieldI2} theorem, 38
\item {\tt filseq_resolve_tac}, \bold{110}
\item {\tt filt_resolve_tac}, 110, 125
\item {\tt filter} constant, 82
\item {\tt Fin.consI} theorem, 48
\item {\tt Fin.emptyI} theorem, 48
\item {\tt Fin_induct} theorem, 48
\item {\tt Fin_mono} theorem, 48
\item {\tt Fin_subset} theorem, 48
\item {\tt Fin_UnI} theorem, 48
\item {\tt Fin_UnionI} theorem, 48
\item first-order logic, 5--22
\item {\tt Fixedpt} theory, 42
\item {\tt flat} constant, 49
\item {\tt flat_def} theorem, 49
\item flex-flex constraints, 104
\item {\tt FOL} theory, 1, 5, 11, 126
\item {\tt FOL_cs}, \bold{11}
\item {\tt FOL_ss}, \bold{6}
\item {\tt foldl} constant, 82
\item {\tt form_rls}, \bold{124}
\item {\tt formL_rls}, \bold{124}
\item {\tt forms_of_seq}, \bold{109}
\item {\tt foundation} theorem, 30
\item {\tt fst} constant, 25, 32, 77, 117, 122
\item {\tt fst_conv} theorem, 37, 77
\item {\tt fst_def} theorem, 31, 122
\item {\tt Fun} theory, 75
\item {\textit {fun}} type, 61
\item {\tt fun_cong} theorem, 65
\item {\tt fun_disjoint_apply1} theorem, 40, 56
\item {\tt fun_disjoint_apply2} theorem, 40
\item {\tt fun_disjoint_Un} theorem, 40, 58
\item {\tt fun_empty} theorem, 40
\item {\tt fun_extension} theorem, 39, 40
\item {\tt fun_is_rel} theorem, 39
\item {\tt fun_single} theorem, 40
\item function applications
\subitem in \CTT, 119
\subitem in \ZF, 25
\indexspace
\item {\tt gfp_def} theorem, 44
\item {\tt gfp_least} theorem, 44
\item {\tt gfp_mono} theorem, 44
\item {\tt gfp_subset} theorem, 44
\item {\tt gfp_Tarski} theorem, 44
\item {\tt gfp_upperbound} theorem, 44
\item {\tt goalw}, 18
\indexspace
\item {\tt hd} constant, 82
\item higher-order logic, 59--103
\item {\tt HOL} theory, 1, 59
\item {\sc hol} system, 59, 62
\item {\tt HOL_basic_ss}, \bold{75}
\item {\tt HOL_cs}, \bold{76}
\item {\tt HOL_quantifiers}, \bold{62}, 70
\item {\tt HOL_ss}, \bold{75}
\item {\tt HOLCF} theory, 1
\item {\tt hyp_rew_tac}, \bold{126}
\item {\tt hyp_subst_tac}, 6, 75
\indexspace
\item {\textit {i}} type, 24, 116
\item {\tt id} constant, 45
\item {\tt id_def} theorem, 45
\item {\tt If} constant, 60
\item {\tt if} constant, 25
\item {\tt if_def} theorem, 17, 30, 64
\item {\tt if_not_P} theorem, 35, 66
\item {\tt if_P} theorem, 35, 66
\item {\tt ifE} theorem, 19
\item {\tt iff} theorem, 63, 64
\item {\tt iff_def} theorem, 8, 107
\item {\tt iff_impE} theorem, 9
\item {\tt iffCE} theorem, 11, 66, 70
\item {\tt iffD1} theorem, 9, 65
\item {\tt iffD2} theorem, 9, 65
\item {\tt iffE} theorem, 9, 65
\item {\tt iffI} theorem, 9, 19, 65
\item {\tt iffL} theorem, 108, 114
\item {\tt iffR} theorem, 108
\item {\tt ifI} theorem, 19
\item {\tt IFOL} theory, 5
\item {\tt IFOL_ss}, \bold{6}
\item {\tt image_def} theorem, 31, 71
\item {\tt imageE} theorem, 38, 73
\item {\tt imageI} theorem, 38, 73
\item {\tt imp_impE} theorem, 9, 14
\item {\tt impCE} theorem, 11, 66
\item {\tt impE} theorem, 9, 10, 65
\item {\tt impI} theorem, 8, 63
\item {\tt impL} theorem, 107
\item {\tt impR} theorem, 107
\item {\tt in} symbol, 27, 61
\item {\textit {ind}} type, 80
\item {\tt induct} theorem, 44
\item {\tt induct_tac}, 81, \bold{88}
\item {\tt inductive}, 96--99
\item {\tt Inf} constant, 25, 29
\item {\tt infinity} theorem, 31
\item {\tt inj} constant, 45, 75
\item {\tt inj_converse_inj} theorem, 45
\item {\tt inj_def} theorem, 45, 75
\item {\tt inj_Inl} theorem, 79
\item {\tt inj_Inr} theorem, 79
\item {\tt inj_onto} constant, 75
\item {\tt inj_onto_def} theorem, 75
\item {\tt inj_Suc} theorem, 79
\item {\tt Inl} constant, 43, 79
\item {\tt inl} constant, 117, 122, 132
\item {\tt Inl_def} theorem, 43
\item {\tt Inl_inject} theorem, 43
\item {\tt Inl_neq_Inr} theorem, 43
\item {\tt Inl_not_Inr} theorem, 79
\item {\tt Inr} constant, 43, 79
\item {\tt inr} constant, 117, 122
\item {\tt Inr_def} theorem, 43
\item {\tt Inr_inject} theorem, 43
\item {\tt insert} constant, 68
\item {\tt insert_def} theorem, 71
\item {\tt insertE} theorem, 73
\item {\tt insertI1} theorem, 73
\item {\tt insertI2} theorem, 73
\item {\tt INT} symbol, 26, 28, 68--70
\item {\tt Int} symbol, 25, 68
\item {\tt Int_absorb} theorem, 41, 74
\item {\tt Int_assoc} theorem, 41, 74
\item {\tt Int_commute} theorem, 41, 74
\item {\tt INT_D} theorem, 73
\item {\tt Int_def} theorem, 30, 71
\item {\tt INT_E} theorem, 34, 73
\item {\tt Int_greatest} theorem, 36, 52, 54, 74
\item {\tt INT_I} theorem, 34, 73
\item {\tt Int_Inter_image} theorem, 74
\item {\tt Int_lower1} theorem, 36, 53, 74
\item {\tt Int_lower2} theorem, 36, 53, 74
\item {\tt Int_Un_distrib} theorem, 41, 74
\item {\tt Int_Union} theorem, 74
\item {\tt Int_Union_RepFun} theorem, 41
\item {\tt IntD1} theorem, 35, 73
\item {\tt IntD2} theorem, 35, 73
\item {\tt IntE} theorem, 35, 53, 73
\item {\tt INTER} constant, 68
\item {\tt Inter} constant, 25, 68
\item {\tt INTER1} constant, 68
\item {\tt INTER1_def} theorem, 71
\item {\tt INTER_def} theorem, 71
\item {\tt Inter_def} theorem, 30, 71
\item {\tt Inter_greatest} theorem, 36, 74
\item {\tt Inter_lower} theorem, 36, 74
\item {\tt Inter_Un_distrib} theorem, 41, 74
\item {\tt InterD} theorem, 34, 73
\item {\tt InterE} theorem, 34, 73
\item {\tt InterI} theorem, 32, 34, 73
\item {\tt IntI} theorem, 35, 73
\item {\tt IntPr.best_tac}, \bold{11}
\item {\tt IntPr.fast_tac}, \bold{10}, 13
\item {\tt IntPr.inst_step_tac}, \bold{10}
\item {\tt IntPr.safe_step_tac}, \bold{10}
\item {\tt IntPr.safe_tac}, \bold{10}
\item {\tt IntPr.step_tac}, \bold{10}
\item {\tt intr_rls}, \bold{124}
\item {\tt intr_tac}, \bold{125}, 134, 135
\item {\tt intrL_rls}, \bold{124}
\item {\tt inv} constant, 75
\item {\tt inv_def} theorem, 75
\indexspace
\item {\tt lam} symbol, 26, 28, 119
\item {\tt lam_def} theorem, 31
\item {\tt lam_type} theorem, 39
\item {\tt Lambda} constant, 25, 29
\item {\tt lambda} constant, 117, 119
\item $\lambda$-abstractions
\subitem in \CTT, 119
\subitem in \ZF, 26
\item {\tt lamE} theorem, 39, 40
\item {\tt lamI} theorem, 39, 40
\item {\tt last} constant, 82
\item {\tt LCF} theory, 1
\item {\tt le_cs}, \bold{23}
\item {\tt LEAST} constant, 61, 62, 80
\item {\tt Least} constant, 60
\item {\tt Least_def} theorem, 64
\item {\tt left_comp_id} theorem, 45
\item {\tt left_comp_inverse} theorem, 45
\item {\tt left_inverse} theorem, 45
\item {\tt length} constant, 49, 82
\item {\tt length_def} theorem, 49
\item {\tt less_induct} theorem, 81
\item {\tt Let} constant, 24, 25, 60, 63
\item {\tt let} symbol, 27, 61, 63
\item {\tt Let_def} theorem, 24, 30, 63, 64
\item {\tt LFilter} theory, 100
\item {\tt lfp_def} theorem, 44
\item {\tt lfp_greatest} theorem, 44
\item {\tt lfp_lowerbound} theorem, 44
\item {\tt lfp_mono} theorem, 44
\item {\tt lfp_subset} theorem, 44
\item {\tt lfp_Tarski} theorem, 44
\item {\tt List} theory, 81, 82
\item {\textit {list}} type, 100
\item {\textit{list}} type, 81
\item {\tt list} constant, 49
\item {\tt List.induct} theorem, 49
\item {\tt list_case} constant, 49
\item {\tt list_mono} theorem, 49
\item {\tt list_rec} constant, 49
\item {\tt list_rec_Cons} theorem, 49
\item {\tt list_rec_def} theorem, 49
\item {\tt list_rec_Nil} theorem, 49
\item {\tt LK} theory, 1, 104, 108
\item {\tt LK_dup_pack}, \bold{110}, 112
\item {\tt LK_pack}, \bold{110}
\item {\tt LList} theory, 100
\item {\tt logic} class, 5
\indexspace
\item {\tt map} constant, 49, 82
\item {\tt map_app_distrib} theorem, 49
\item {\tt map_compose} theorem, 49
\item {\tt map_def} theorem, 49
\item {\tt map_flat} theorem, 49
\item {\tt map_ident} theorem, 49
\item {\tt map_type} theorem, 49
\item {\tt max} constant, 61, 80
\item {\tt mem} symbol, 82
\item {\tt mem_asym} theorem, 35, 36
\item {\tt mem_Collect_eq} theorem, 70, 71
\item {\tt mem_irrefl} theorem, 35
\item {\tt min} constant, 61, 80
\item {\tt minus} class, 61
\item {\tt mod} symbol, 47, 79, 128
\item {\tt mod_def} theorem, 47, 128
\item {\tt mod_geq} theorem, 80
\item {\tt mod_less} theorem, 80
\item {\tt mod_quo_equality} theorem, 47
\item {\tt Modal} theory, 1
\item {\tt mono} constant, 61
\item {\tt mp} theorem, 8, 63
\item {\tt mp_tac}, \bold{10}, \bold{126}
\item {\tt mult_0} theorem, 47
\item {\tt mult_assoc} theorem, 47, 128
\item {\tt mult_commute} theorem, 47, 128
\item {\tt mult_def} theorem, 47, 128
\item {\tt mult_succ} theorem, 47
\item {\tt mult_type} theorem, 47
\item {\tt mult_typing} theorem, 128
\item {\tt multC0} theorem, 128
\item {\tt multC_succ} theorem, 128
\indexspace
\item {\tt N} constant, 117
\item {\tt n_not_Suc_n} theorem, 79
\item {\tt Nat} theory, 46, 80
\item {\textit {nat}} type, 79, 80, 88, 89
\item {\textit{nat}} type, 80--81
\item {\tt nat} constant, 47
\item {\tt nat_0I} theorem, 47
\item {\tt nat_case} constant, 47
\item {\tt nat_case_0} theorem, 47
\item {\tt nat_case_def} theorem, 47
\item {\tt nat_case_succ} theorem, 47
\item {\tt nat_def} theorem, 47
\item {\tt nat_induct} theorem, 47, 79
\item {\tt nat_rec} constant, 81
\item {\tt nat_succI} theorem, 47
\item {\tt NatDef} theory, 80
\item {\tt NC0} theorem, 121
\item {\tt NC_succ} theorem, 121
\item {\tt NE} theorem, 120, 121, 129
\item {\tt NEL} theorem, 121
\item {\tt NF} theorem, 121, 130
\item {\tt NI0} theorem, 121
\item {\tt NI_succ} theorem, 121
\item {\tt NI_succL} theorem, 121
\item {\tt Nil_Cons_iff} theorem, 49
\item {\tt NilI} theorem, 49
\item {\tt NIO} theorem, 129
\item {\tt Not} constant, 7, 60, 105
\item {\tt not_def} theorem, 8, 42, 64
\item {\tt not_impE} theorem, 9
\item {\tt not_sym} theorem, 65
\item {\tt notE} theorem, 9, 10, 65
\item {\tt notI} theorem, 9, 65
\item {\tt notL} theorem, 107
\item {\tt notnotD} theorem, 11, 66
\item {\tt notR} theorem, 107
\item {\tt nth} constant, 82
\item {\tt null} constant, 82
\indexspace
\item {\tt O} symbol, 45
\item {\textit {o}} type, 5, 104
\item {\tt o} symbol, 60, 71
\item {\tt o_def} theorem, 64
\item {\tt of} symbol, 63
\item {\tt or_def} theorem, 42, 64
\item {\tt Ord} theory, 61
\item {\tt ord} class, 61, 62, 80
\item {\tt order} class, 61, 80
\indexspace
\item {\tt pack} ML type, 110
\item {\tt Pair} constant, 25, 26, 77
\item {\tt pair} constant, 117
\item {\tt Pair_def} theorem, 31
\item {\tt Pair_eq} theorem, 77
\item {\tt Pair_inject} theorem, 37, 77
\item {\tt Pair_inject1} theorem, 37
\item {\tt Pair_inject2} theorem, 37
\item {\tt Pair_neq_0} theorem, 37
\item {\tt PairE} theorem, 77
\item {\tt pairing} theorem, 34
\item {\tt pc_tac}, \bold{111}, \bold{127}, 133, 134
\item {\tt Perm} theory, 42
\item {\tt Pi} constant, 25, 28, 40
\item {\tt Pi_def} theorem, 31
\item {\tt Pi_type} theorem, 39, 40
\item {\tt plus} class, 61
\item {\tt PlusC_inl} theorem, 123
\item {\tt PlusC_inr} theorem, 123
\item {\tt PlusE} theorem, 123, 127, 131
\item {\tt PlusEL} theorem, 123
\item {\tt PlusF} theorem, 123
\item {\tt PlusFL} theorem, 123
\item {\tt PlusI_inl} theorem, 123, 132
\item {\tt PlusI_inlL} theorem, 123
\item {\tt PlusI_inr} theorem, 123
\item {\tt PlusI_inrL} theorem, 123
\item {\tt Pow} constant, 25, 68
\item {\tt Pow_def} theorem, 71
\item {\tt Pow_iff} theorem, 30
\item {\tt Pow_mono} theorem, 52
\item {\tt PowD} theorem, 33, 53, 73
\item {\tt PowI} theorem, 33, 53, 73
\item {\tt primrec}, 92--93
\item {\tt primrec} symbol, 80
\item {\tt PrimReplace} constant, 25, 29
\item priorities, 2
\item {\tt PROD} symbol, 26, 28, 118, 119
\item {\tt Prod} constant, 117
\item {\tt Prod} theory, 76
\item {\tt ProdC} theorem, 121, 137
\item {\tt ProdC2} theorem, 121
\item {\tt ProdE} theorem, 121, 134, 136, 138
\item {\tt ProdEL} theorem, 121
\item {\tt ProdF} theorem, 121
\item {\tt ProdFL} theorem, 121
\item {\tt ProdI} theorem, 121, 127, 129
\item {\tt ProdIL} theorem, 121
\item {\tt prop_cs}, \bold{11}, \bold{76}
\item {\tt prop_pack}, \bold{110}
\indexspace
\item {\tt qcase_def} theorem, 43
\item {\tt qconverse} constant, 42
\item {\tt qconverse_def} theorem, 43
\item {\tt qed_spec_mp}, 89
\item {\tt qfsplit_def} theorem, 43
\item {\tt QInl_def} theorem, 43
\item {\tt QInr_def} theorem, 43
\item {\tt QPair} theory, 42
\item {\tt QPair_def} theorem, 43
\item {\tt QSigma} constant, 42
\item {\tt QSigma_def} theorem, 43
\item {\tt qsplit} constant, 42
\item {\tt qsplit_def} theorem, 43
\item {\tt qsum_def} theorem, 43
\item {\tt QUniv} theory, 46
\indexspace
\item {\tt range} constant, 25, 68, 101
\item {\tt range_def} theorem, 31, 71
\item {\tt range_of_fun} theorem, 39, 40
\item {\tt range_subset} theorem, 38
\item {\tt range_type} theorem, 39
\item {\tt rangeE} theorem, 38, 73, 101
\item {\tt rangeI} theorem, 38, 73
\item {\tt rank} constant, 48
\item {\tt rank_ss}, \bold{23}
\item {\tt rec} constant, 47, 117, 120
\item {\tt rec_0} theorem, 47
\item {\tt rec_def} theorem, 47
\item {\tt rec_succ} theorem, 47
\item {\tt recdef}, 93--96
\item recursion
\subitem general, 93--96
\subitem primitive, 92--93
\item recursive functions, \see{recursion}{91}
\item {\tt red_if_equal} theorem, 120
\item {\tt Reduce} constant, 117, 120, 126
\item {\tt refl} theorem, 8, 63, 107
\item {\tt refl_elem} theorem, 120, 124
\item {\tt refl_red} theorem, 120
\item {\tt refl_type} theorem, 120, 124
\item {\tt REPEAT_FIRST}, 125
\item {\tt repeat_goal_tac}, \bold{111}
\item {\tt RepFun} constant, 25, 28, 29, 32
\item {\tt RepFun_def} theorem, 30
\item {\tt RepFunE} theorem, 34
\item {\tt RepFunI} theorem, 34
\item {\tt Replace} constant, 25, 28, 29, 32
\item {\tt Replace_def} theorem, 30
\item {\tt replace_type} theorem, 124, 136
\item {\tt ReplaceE} theorem, 34
\item {\tt ReplaceI} theorem, 34
\item {\tt replacement} theorem, 30
\item {\tt reresolve_tac}, \bold{111}
\item {\tt res_inst_tac}, 62
\item {\tt restrict} constant, 25, 32
\item {\tt restrict} theorem, 39
\item {\tt restrict_bij} theorem, 45
\item {\tt restrict_def} theorem, 31
\item {\tt restrict_type} theorem, 39
\item {\tt rev} constant, 49, 82
\item {\tt rev_def} theorem, 49
\item {\tt rew_tac}, 18, \bold{126}
\item {\tt rewrite_rule}, 19
\item {\tt right_comp_id} theorem, 45
\item {\tt right_comp_inverse} theorem, 45
\item {\tt right_inverse} theorem, 45
\item {\tt RL}, 131
\item {\tt RS}, 136, 138
\indexspace
\item {\tt safe_goal_tac}, \bold{112}
\item {\tt safe_tac}, \bold{127}
\item {\tt safestep_tac}, \bold{127}
\item search
\subitem best-first, 103
\item {\tt select_equality} theorem, 64, 66
\item {\tt selectI} theorem, 63, 64
\item {\tt separation} theorem, 34
\item {\tt Seqof} constant, 105
\item sequent calculus, 104--115
\item {\tt Set} theory, 67, 70
\item {\tt set} constant, 82
\item {\tt set} type, 67
\item set theory, 23--58
\item {\tt set_current_thy}, 103
\item {\tt set_diff_def} theorem, 71
\item {\tt show_sorts}, 62
\item {\tt show_types}, 62
\item {\tt Sigma} constant, 25, 28, 29, 37, 77
\item {\tt Sigma_def} theorem, 31, 77
\item {\tt SigmaE} theorem, 37, 77
\item {\tt SigmaE2} theorem, 37
\item {\tt SigmaI} theorem, 37, 77
\item simplification
\subitem of conjunctions, 6, 75
\item {\tt singletonE} theorem, 35
\item {\tt singletonI} theorem, 35
\item {\tt size} constant, 87
\item {\tt snd} constant, 25, 32, 77, 117, 122
\item {\tt snd_conv} theorem, 37, 77
\item {\tt snd_def} theorem, 31, 122
\item {\tt sobj} type, 106
\item {\tt spec} theorem, 8, 66
\item {\tt split} constant, 25, 32, 77, 117, 131
\item {\tt split} theorem, 37, 77
\item {\tt split_all_tac}, \bold{78}
\item {\tt split_def} theorem, 31
\item {\tt ssubst} theorem, 9, 65, 67
\item {\tt stac}, \bold{75}
\item {\tt Step_tac}, 22
\item {\tt step_tac}, 22, \bold{112}, \bold{127}
\item {\tt strip_tac}, \bold{67}
\item {\tt subset_def} theorem, 30, 71
\item {\tt subset_refl} theorem, 33, 72
\item {\tt subset_trans} theorem, 33, 72
\item {\tt subsetCE} theorem, 33, 70, 72
\item {\tt subsetD} theorem, 33, 55, 70, 72
\item {\tt subsetI} theorem, 33, 53, 54, 72
\item {\tt subst} theorem, 8, 63
\item {\tt subst_elem} theorem, 120
\item {\tt subst_elemL} theorem, 120
\item {\tt subst_eqtyparg} theorem, 124, 136
\item {\tt subst_prodE} theorem, 122, 124
\item {\tt subst_type} theorem, 120
\item {\tt subst_typeL} theorem, 120
\item {\tt Suc} constant, 79
\item {\tt Suc_not_Zero} theorem, 79
\item {\tt succ} constant, 25, 29, 117
\item {\tt succ_def} theorem, 31
\item {\tt succ_inject} theorem, 35
\item {\tt succ_neq_0} theorem, 35
\item {\tt succCI} theorem, 35
\item {\tt succE} theorem, 35
\item {\tt succI1} theorem, 35
\item {\tt succI2} theorem, 35
\item {\tt SUM} symbol, 26, 28, 118, 119
\item {\tt Sum} constant, 117
\item {\tt Sum} theory, 42, 78
\item {\tt sum_case} constant, 79
\item {\tt sum_case_Inl} theorem, 79
\item {\tt sum_case_Inr} theorem, 79
\item {\tt sum_def} theorem, 43
\item {\tt sum_InlI} theorem, 43
\item {\tt sum_InrI} theorem, 43
\item {\tt SUM_Int_distrib1} theorem, 41
\item {\tt SUM_Int_distrib2} theorem, 41
\item {\tt SUM_Un_distrib1} theorem, 41
\item {\tt SUM_Un_distrib2} theorem, 41
\item {\tt SumC} theorem, 122
\item {\tt SumE} theorem, 122, 127, 131
\item {\tt sumE} theorem, 79
\item {\tt sumE2} theorem, 43
\item {\tt SumE_fst} theorem, 122, 124, 136, 137
\item {\tt SumE_snd} theorem, 122, 124, 138
\item {\tt SumEL} theorem, 122
\item {\tt SumF} theorem, 122
\item {\tt SumFL} theorem, 122
\item {\tt SumI} theorem, 122, 132
\item {\tt SumIL} theorem, 122
\item {\tt SumIL2} theorem, 124
\item {\tt surj} constant, 45, 71, 75
\item {\tt surj_def} theorem, 45, 75
\item {\tt surjective_pairing} theorem, 77
\item {\tt surjective_sum} theorem, 79
\item {\tt swap} theorem, 11, 66
\item {\tt swap_res_tac}, 16, 102
\item {\tt sym} theorem, 9, 65, 107
\item {\tt sym_elem} theorem, 120
\item {\tt sym_type} theorem, 120
\item {\tt symL} theorem, 108
\indexspace
\item {\tt T} constant, 117
\item {\textit {t}} type, 116
\item {\tt take} constant, 82
\item {\tt takeWhile} constant, 82
\item {\tt TC} theorem, 123
\item {\tt TE} theorem, 123
\item {\tt TEL} theorem, 123
\item {\tt term} class, 5, 61, 104
\item {\tt test_assume_tac}, \bold{125}
\item {\tt TF} theorem, 123
\item {\tt THE} symbol, 26, 28, 36, 105
\item {\tt The} constant, 25, 28, 29, 105
\item {\tt The} theorem, 107
\item {\tt the_def} theorem, 30
\item {\tt the_equality} theorem, 35, 36
\item {\tt theI} theorem, 35, 36
\item {\tt thinL} theorem, 107
\item {\tt thinR} theorem, 107
\item {\tt TI} theorem, 123
\item {\tt times} class, 61
\item {\tt tl} constant, 82
\item tracing
\subitem of unification, 62
\item {\tt trans} theorem, 9, 65, 107
\item {\tt trans_elem} theorem, 120
\item {\tt trans_red} theorem, 120
\item {\tt trans_tac}, 81
\item {\tt trans_type} theorem, 120
\item {\tt True} constant, 7, 60, 105
\item {\tt True_def} theorem, 8, 64, 107
\item {\tt True_or_False} theorem, 63, 64
\item {\tt TrueI} theorem, 9, 65
\item {\tt Trueprop} constant, 7, 60, 105
\item {\tt TrueR} theorem, 108
\item {\tt tt} constant, 117
\item {\tt Type} constant, 117
\item type definition, \bold{84}
\item {\tt typechk_tac}, \bold{125}, 130, 133, 137, 138
\item {\tt typedef}, 81
\indexspace
\item {\tt UN} symbol, 26, 28, 68--70
\item {\tt Un} symbol, 25, 68
\item {\tt Un1} theorem, 70
\item {\tt Un2} theorem, 70
\item {\tt Un_absorb} theorem, 41, 74
\item {\tt Un_assoc} theorem, 41, 74
\item {\tt Un_commute} theorem, 41, 74
\item {\tt Un_def} theorem, 30, 71
\item {\tt UN_E} theorem, 34, 73
\item {\tt UN_I} theorem, 34, 73
\item {\tt Un_Int_distrib} theorem, 41, 74
\item {\tt Un_Inter} theorem, 74
\item {\tt Un_Inter_RepFun} theorem, 41
\item {\tt Un_least} theorem, 36, 74
\item {\tt Un_Union_image} theorem, 74
\item {\tt Un_upper1} theorem, 36, 74
\item {\tt Un_upper2} theorem, 36, 74
\item {\tt UnCI} theorem, 35, 36, 70, 73
\item {\tt UnE} theorem, 35, 73
\item {\tt UnI1} theorem, 35, 36, 57, 73
\item {\tt UnI2} theorem, 35, 36, 73
\item unification
\subitem incompleteness of, 62
\item {\tt Unify.trace_types}, 62
\item {\tt UNION} constant, 68
\item {\tt Union} constant, 25, 68
\item {\tt UNION1} constant, 68
\item {\tt UNION1_def} theorem, 71
\item {\tt UNION_def} theorem, 71
\item {\tt Union_def} theorem, 71
\item {\tt Union_iff} theorem, 30
\item {\tt Union_least} theorem, 36, 74
\item {\tt Union_Un_distrib} theorem, 41, 74
\item {\tt Union_upper} theorem, 36, 74
\item {\tt UnionE} theorem, 34, 55, 73
\item {\tt UnionI} theorem, 34, 55, 73
\item {\tt unit_eq} theorem, 78
\item {\tt Univ} theory, 46
\item {\tt Upair} constant, 24, 25, 29
\item {\tt Upair_def} theorem, 30
\item {\tt UpairE} theorem, 34
\item {\tt UpairI1} theorem, 34
\item {\tt UpairI2} theorem, 34
\indexspace
\item {\tt vimage_def} theorem, 31
\item {\tt vimageE} theorem, 38
\item {\tt vimageI} theorem, 38
\indexspace
\item {\tt when} constant, 117, 122, 131
\indexspace
\item {\tt xor_def} theorem, 42
\indexspace
\item {\tt zero_ne_succ} theorem, 120, 121
\item {\tt ZF} theory, 1, 23, 59
\item {\tt ZF_cs}, \bold{23}
\item {\tt ZF_ss}, \bold{23}
\end{theindex}