# HG changeset patch # User wenzelm # Date 863199729 -7200 # Node ID a8faa68c68b52c99ab0f93b0c4b3125931702b09 # Parent 434b33c5f827929566c9c70f55c6c4ee1457a391 SYNC; diff -r 434b33c5f827 -r a8faa68c68b5 doc-src/Logics/logics.ind --- a/doc-src/Logics/logics.ind Fri May 09 19:41:46 1997 +0200 +++ b/doc-src/Logics/logics.ind Fri May 09 19:42:09 1997 +0200 @@ -1,164 +1,166 @@ \begin{theindex} - \item {\tt !} symbol, 58, 60, 66, 68 - \item {\tt[]} symbol, 79 - \item {\tt\#} symbol, 79 - \item {\tt\#*} symbol, 46, 121 - \item {\tt\#+} symbol, 46, 121 + \item {\tt !} symbol, 59, 61, 68, 69 + \item {\tt[]} symbol, 80 + \item {\tt\#} symbol, 80 + \item {\tt\#*} symbol, 46, 122 + \item {\tt\#+} symbol, 46, 122 \item {\tt\#-} symbol, 46 - \item {\tt\&} symbol, 6, 58, 98 - \item {\tt *} symbol, 25, 59, 76, 112 - \item {\tt *} type, 74 - \item {\tt +} symbol, 42, 59, 76, 112 - \item {\tt +} type, 74 - \item {\tt -} symbol, 24, 59, 76, 121 - \item {\tt -->} symbol, 6, 58, 98, 112 + \item {\tt\&} symbol, 6, 59, 99 + \item {\tt *} symbol, 25, 60, 77, 113 + \item {\tt *} type, 75 + \item {\tt +} symbol, 42, 60, 77, 113 + \item {\tt +} type, 75 + \item {\tt -} symbol, 24, 60, 77, 122 + \item {\tt -->} symbol, 6, 59, 99, 113 \item {\tt ->} symbol, 25 \item {\tt -``} symbol, 24 - \item {\tt :} symbol, 24, 65 - \item {\tt <} constant, 75 - \item {\tt <} symbol, 76 - \item {\tt <->} symbol, 6, 98 - \item {\tt <=} constant, 75 - \item {\tt <=} symbol, 24, 65 - \item {\tt =} symbol, 6, 58, 98, 112 - \item {\tt ?} symbol, 58, 60, 66, 68 - \item {\tt ?!} symbol, 58 - \item {\tt\at} symbol, 58, 79 - \item {\tt `} symbol, 24, 112 - \item {\tt ``} symbol, 24, 65 - \item \verb'{}' symbol, 65 - \item {\tt |} symbol, 6, 58, 98 - \item {\tt |-|} symbol, 121 + \item {\tt :} symbol, 24, 67 + \item {\tt <} constant, 78 + \item {\tt <} symbol, 77 + \item {\tt <->} symbol, 6, 99 + \item {\tt <=} constant, 78 + \item {\tt <=} symbol, 24, 67 + \item {\tt =} symbol, 6, 59, 99, 113 + \item {\tt ?} symbol, 59, 61, 68, 69 + \item {\tt ?!} symbol, 59 + \item {\tt\at} symbol, 59, 80 + \item {\tt `} symbol, 24, 113 + \item {\tt ``} symbol, 24, 67 + \item \verb'{}' symbol, 67 + \item {\tt |} symbol, 6, 59, 99 + \item {\tt |-|} symbol, 122 \indexspace - \item {\tt 0} constant, 24, 76, 110 + \item {\tt 0} constant, 24, 77, 111 \indexspace - \item {\tt absdiff_def} theorem, 121 - \item {\tt add_assoc} theorem, 121 - \item {\tt add_commute} theorem, 121 - \item {\tt add_def} theorem, 46, 121 - \item {\tt add_inverse_diff} theorem, 121 - \item {\tt add_mp_tac}, \bold{119} - \item {\tt add_mult_dist} theorem, 46, 121 - \item {\tt add_safes}, \bold{104} - \item {\tt add_typing} theorem, 121 - \item {\tt add_unsafes}, \bold{104} - \item {\tt addC0} theorem, 121 - \item {\tt addC_succ} theorem, 121 - \item {\tt ALL} symbol, 6, 25, 58, 60, 66, 68, 98 - \item {\tt All} constant, 6, 58, 98 - \item {\tt All_def} theorem, 62 - \item {\tt all_dupE} theorem, 4, 8, 64 + \item {\tt absdiff_def} theorem, 122 + \item {\tt add_assoc} theorem, 122 + \item {\tt add_commute} theorem, 122 + \item {\tt add_def} theorem, 46, 122 + \item {\tt add_inverse_diff} theorem, 122 + \item {\tt add_mp_tac}, \bold{120} + \item {\tt add_mult_dist} theorem, 46, 122 + \item {\tt add_safes}, \bold{105} + \item {\tt add_typing} theorem, 122 + \item {\tt add_unsafes}, \bold{105} + \item {\tt addC0} theorem, 122 + \item {\tt addC_succ} theorem, 122 + \item {\tt ALL} symbol, 6, 25, 59, 61, 68, 69, 99 + \item {\tt All} constant, 6, 59, 99 + \item {\tt All_def} theorem, 63 + \item {\tt all_dupE} theorem, 4, 8, 65 \item {\tt all_impE} theorem, 8 - \item {\tt allE} theorem, 4, 8, 64 - \item {\tt allI} theorem, 7, 64 - \item {\tt allL} theorem, 100, 103 - \item {\tt allL_thin} theorem, 101 - \item {\tt allR} theorem, 100 - \item {\tt and_def} theorem, 41, 62 + \item {\tt allE} theorem, 4, 8, 65 + \item {\tt allI} theorem, 7, 65 + \item {\tt allL} theorem, 101, 104 + \item {\tt allL_thin} theorem, 102 + \item {\tt allR} theorem, 101 + \item {\tt and_def} theorem, 41, 63 \item {\tt app_def} theorem, 48 \item {\tt apply_def} theorem, 30 - \item {\tt apply_equality} theorem, 38, 39, 55 + \item {\tt apply_equality} theorem, 38, 39, 56 \item {\tt apply_equality2} theorem, 38 \item {\tt apply_iff} theorem, 38 - \item {\tt apply_Pair} theorem, 38, 55, 56 + \item {\tt apply_Pair} theorem, 38, 56 \item {\tt apply_type} theorem, 38 - \item {\tt arg_cong} theorem, 63 - \item {\tt Arith} theory, 45, 77, 120 + \item {\tt arg_cong} theorem, 64 + \item {\tt Arith} theory, 45, 78, 121 \item assumptions \subitem contradictory, 15 - \subitem in {\CTT}, 109, 119 + \subitem in {\CTT}, 110, 120 \indexspace - \item {\tt Ball} constant, 24, 28, 65, 68 + \item {\tt Ball} constant, 24, 28, 67, 69 \item {\tt ball_cong} theorem, 31, 32 - \item {\tt Ball_def} theorem, 29, 68 - \item {\tt ballE} theorem, 31, 32, 69 - \item {\tt ballI} theorem, 32, 69 - \item {\tt basic} theorem, 100 - \item {\tt basic_defs}, \bold{117} - \item {\tt best_tac}, \bold{105} + \item {\tt Ball_def} theorem, 29, 70 + \item {\tt ballE} theorem, 31, 32, 71 + \item {\tt ballI} theorem, 32, 71 + \item {\tt basic} theorem, 101 + \item {\tt basic_defs}, \bold{118} + \item {\tt best_tac}, \bold{106} \item {\tt beta} theorem, 38, 39 - \item {\tt Bex} constant, 24, 28, 65, 68 + \item {\tt Bex} constant, 24, 28, 67, 69 \item {\tt bex_cong} theorem, 31, 32 - \item {\tt Bex_def} theorem, 29, 68 - \item {\tt bexCI} theorem, 32, 69, 72 - \item {\tt bexE} theorem, 32, 69 - \item {\tt bexI} theorem, 32, 69, 72 + \item {\tt Bex_def} theorem, 29, 70 + \item {\tt bexCI} theorem, 32, 69, 71 + \item {\tt bexE} theorem, 32, 71 + \item {\tt bexI} theorem, 32, 69, 71 \item {\tt bij} constant, 44 \item {\tt bij_converse_bij} theorem, 44 \item {\tt bij_def} theorem, 44 \item {\tt bij_disjoint_Un} theorem, 44 + \item {\tt Blast_tac}, 53--55 + \item {\tt blast_tac}, 17, 19, 20 \item {\tt bnd_mono_def} theorem, 43 \item {\tt Bool} theory, 39 - \item {\tt bool} type, 59 + \item {\tt bool} type, 60 \item {\tt bool_0I} theorem, 41 \item {\tt bool_1I} theorem, 41 \item {\tt bool_def} theorem, 41 \item {\tt boolE} theorem, 41 - \item {\tt box_equals} theorem, 62, 63 - \item {\tt bspec} theorem, 32, 69 + \item {\tt box_equals} theorem, 64, 66 + \item {\tt bspec} theorem, 32, 71 \indexspace \item {\tt case} constant, 42 - \item {\tt case} symbol, 61, 77, 78, 84 + \item {\tt case} symbol, 62, 78, 79, 85 \item {\tt case_def} theorem, 42 \item {\tt case_Inl} theorem, 42 \item {\tt case_Inr} theorem, 42 - \item {\tt case_tac}, \bold{62} + \item {\tt case_tac}, \bold{66} \item {\tt CCL} theory, 1 - \item {\tt ccontr} theorem, 64 - \item {\tt classical} theorem, 64 + \item {\tt ccontr} theorem, 65 + \item {\tt classical} theorem, 65 \item {\tt coinduct} theorem, 43 - \item {\tt coinductive}, 90--93 - \item {\tt Collect} constant, 24, 25, 28, 65, 67 + \item {\tt coinductive}, 91--94 + \item {\tt Collect} constant, 24, 25, 28, 67, 69 \item {\tt Collect_def} theorem, 29 - \item {\tt Collect_mem_eq} theorem, 68 + \item {\tt Collect_mem_eq} theorem, 69, 70 \item {\tt Collect_subset} theorem, 35 - \item {\tt CollectD} theorem, 69, 95 + \item {\tt CollectD} theorem, 71, 96 \item {\tt CollectD1} theorem, 31, 33 \item {\tt CollectD2} theorem, 31, 33 - \item {\tt CollectE} theorem, 31, 33, 69 - \item {\tt CollectI} theorem, 33, 69, 96 + \item {\tt CollectE} theorem, 31, 33, 71 + \item {\tt CollectI} theorem, 33, 71, 97 \item {\tt comp_assoc} theorem, 44 \item {\tt comp_bij} theorem, 44 \item {\tt comp_def} theorem, 44 \item {\tt comp_func} theorem, 44 \item {\tt comp_func_apply} theorem, 44 \item {\tt comp_inj} theorem, 44 - \item {\tt comp_rls}, \bold{117} + \item {\tt comp_rls}, \bold{118} \item {\tt comp_surj} theorem, 44 \item {\tt comp_type} theorem, 44 - \item {\tt Compl} constant, 65 - \item {\tt Compl_def} theorem, 68 - \item {\tt Compl_disjoint} theorem, 71 - \item {\tt Compl_Int} theorem, 71 - \item {\tt Compl_partition} theorem, 71 - \item {\tt Compl_Un} theorem, 71 - \item {\tt ComplD} theorem, 70 - \item {\tt ComplI} theorem, 70 - \item {\tt concat} constant, 79 + \item {\tt Compl} constant, 67 + \item {\tt Compl_def} theorem, 70 + \item {\tt Compl_disjoint} theorem, 73 + \item {\tt Compl_Int} theorem, 73 + \item {\tt Compl_partition} theorem, 73 + \item {\tt Compl_Un} theorem, 73 + \item {\tt ComplD} theorem, 72 + \item {\tt ComplI} theorem, 72 + \item {\tt concat} constant, 80 \item {\tt cond_0} theorem, 41 \item {\tt cond_1} theorem, 41 \item {\tt cond_def} theorem, 41 - \item {\tt cong} theorem, 63 + \item {\tt cong} theorem, 64 \item congruence rules, 31 - \item {\tt conj_cong}, 73 - \item {\tt conj_impE} theorem, 5, 8 - \item {\tt conjE} theorem, 8, 63 - \item {\tt conjI} theorem, 7, 63 - \item {\tt conjL} theorem, 100 - \item {\tt conjR} theorem, 100 - \item {\tt conjunct1} theorem, 7, 63 - \item {\tt conjunct2} theorem, 7, 63 - \item {\tt conL} theorem, 101 - \item {\tt conR} theorem, 101 + \item {\tt conj_cong}, 5, 74 + \item {\tt conj_impE} theorem, 8, 9 + \item {\tt conjE} theorem, 8, 64 + \item {\tt conjI} theorem, 7, 64 + \item {\tt conjL} theorem, 101 + \item {\tt conjR} theorem, 101 + \item {\tt conjunct1} theorem, 7, 64 + \item {\tt conjunct2} theorem, 7, 64 + \item {\tt conL} theorem, 102 + \item {\tt conR} theorem, 102 \item {\tt cons} constant, 24, 25 \item {\tt cons_def} theorem, 30 \item {\tt Cons_iff} theorem, 48 @@ -167,52 +169,52 @@ \item {\tt ConsI} theorem, 48 \item {\tt consI1} theorem, 34 \item {\tt consI2} theorem, 34 - \item Constructive Type Theory, 109--131 - \item {\tt contr} constant, 110 + \item Constructive Type Theory, 110--132 + \item {\tt contr} constant, 111 \item {\tt converse} constant, 24, 38 \item {\tt converse_def} theorem, 30 - \item {\tt could_res}, \bold{102} - \item {\tt could_resolve_seq}, \bold{103} - \item {\tt CTT} theory, 1, 109 + \item {\tt could_res}, \bold{103} + \item {\tt could_resolve_seq}, \bold{104} + \item {\tt CTT} theory, 1, 110 \item {\tt Cube} theory, 1 - \item {\tt cut} theorem, 100 - \item {\tt cut_facts_tac}, 17, 18, 54 - \item {\tt cutL_tac}, \bold{102} - \item {\tt cutR_tac}, \bold{102} + \item {\tt cut} theorem, 101 + \item {\tt cut_facts_tac}, 17, 18, 55 + \item {\tt cutL_tac}, \bold{103} + \item {\tt cutR_tac}, \bold{103} \indexspace - \item {\tt datatype}, 83--90 + \item {\tt datatype}, 84--91 \item {\tt deepen_tac}, 15 - \item {\tt diff_0_eq_0} theorem, 121 + \item {\tt diff_0_eq_0} theorem, 122 \item {\tt Diff_cancel} theorem, 40 \item {\tt Diff_contains} theorem, 35 \item {\tt Diff_def} theorem, 29 - \item {\tt diff_def} theorem, 46, 121 + \item {\tt diff_def} theorem, 46, 122 \item {\tt Diff_disjoint} theorem, 40 \item {\tt Diff_Int} theorem, 40 \item {\tt Diff_partition} theorem, 40 - \item {\tt diff_self_eq_0} theorem, 121 + \item {\tt diff_self_eq_0} theorem, 122 \item {\tt Diff_subset} theorem, 35 - \item {\tt diff_succ_succ} theorem, 121 - \item {\tt diff_typing} theorem, 121 + \item {\tt diff_succ_succ} theorem, 122 + \item {\tt diff_typing} theorem, 122 \item {\tt Diff_Un} theorem, 40 - \item {\tt diffC0} theorem, 121 + \item {\tt diffC0} theorem, 122 \item {\tt DiffD1} theorem, 34 \item {\tt DiffD2} theorem, 34 \item {\tt DiffE} theorem, 34 \item {\tt DiffI} theorem, 34 - \item {\tt disj_impE} theorem, 5, 8, 13 - \item {\tt disjCI} theorem, 10, 64 - \item {\tt disjE} theorem, 7, 63 - \item {\tt disjI1} theorem, 7, 63 - \item {\tt disjI2} theorem, 7, 63 - \item {\tt disjL} theorem, 100 - \item {\tt disjR} theorem, 100 - \item {\tt div} symbol, 46, 76, 121 - \item {\tt div_def} theorem, 46, 121 - \item {\tt div_geq} theorem, 77 - \item {\tt div_less} theorem, 77 + \item {\tt disj_impE} theorem, 8, 9, 13 + \item {\tt disjCI} theorem, 10, 65 + \item {\tt disjE} theorem, 7, 64 + \item {\tt disjI1} theorem, 7, 64 + \item {\tt disjI2} theorem, 7, 64 + \item {\tt disjL} theorem, 101 + \item {\tt disjR} theorem, 101 + \item {\tt div} symbol, 46, 77, 122 + \item {\tt div_def} theorem, 46, 122 + \item {\tt div_geq} theorem, 78 + \item {\tt div_less} theorem, 78 \item {\tt domain} constant, 24, 38 \item {\tt domain_def} theorem, 30 \item {\tt domain_of_fun} theorem, 38 @@ -220,78 +222,78 @@ \item {\tt domain_type} theorem, 38 \item {\tt domainE} theorem, 37, 38 \item {\tt domainI} theorem, 37, 38 - \item {\tt double_complement} theorem, 40, 71 + \item {\tt double_complement} theorem, 40, 73 \item {\tt dresolve_tac}, 52 - \item {\tt drop} constant, 79 - \item {\tt dropWhile} constant, 79 + \item {\tt drop} constant, 80 + \item {\tt dropWhile} constant, 80 \indexspace - \item {\tt Elem} constant, 110 - \item {\tt elim_rls}, \bold{117} - \item {\tt elimL_rls}, \bold{117} - \item {\tt empty_def} theorem, 68 - \item {\tt empty_pack}, \bold{103} + \item {\tt Elem} constant, 111 + \item {\tt elim_rls}, \bold{118} + \item {\tt elimL_rls}, \bold{118} + \item {\tt empty_def} theorem, 70 + \item {\tt empty_pack}, \bold{104} \item {\tt empty_subsetI} theorem, 32 - \item {\tt emptyE} theorem, 32, 70 - \item {\tt Eps} constant, 58, 60 - \item {\tt Eq} constant, 110 - \item {\tt eq} constant, 110, 115 + \item {\tt emptyE} theorem, 32, 72 + \item {\tt Eps} constant, 59, 61 + \item {\tt Eq} constant, 111 + \item {\tt eq} constant, 111, 116 \item {\tt eq_mp_tac}, \bold{9} - \item {\tt EqC} theorem, 116 - \item {\tt EqE} theorem, 116 - \item {\tt Eqelem} constant, 110 - \item {\tt EqF} theorem, 116 - \item {\tt EqFL} theorem, 116 - \item {\tt EqI} theorem, 116 - \item {\tt Eqtype} constant, 110 - \item {\tt equal_tac}, \bold{118} - \item {\tt equal_types} theorem, 113 - \item {\tt equal_typesL} theorem, 113 - \item {\tt equalityCE} theorem, 69, 72, 95, 96 - \item {\tt equalityD1} theorem, 32, 69 - \item {\tt equalityD2} theorem, 32, 69 - \item {\tt equalityE} theorem, 32, 69 - \item {\tt equalityI} theorem, 32, 51, 53, 69 + \item {\tt EqC} theorem, 117 + \item {\tt EqE} theorem, 117 + \item {\tt Eqelem} constant, 111 + \item {\tt EqF} theorem, 117 + \item {\tt EqFL} theorem, 117 + \item {\tt EqI} theorem, 117 + \item {\tt Eqtype} constant, 111 + \item {\tt equal_tac}, \bold{119} + \item {\tt equal_types} theorem, 114 + \item {\tt equal_typesL} theorem, 114 + \item {\tt equalityCE} theorem, 69, 71, 96, 97 + \item {\tt equalityD1} theorem, 32, 71 + \item {\tt equalityD2} theorem, 32, 71 + \item {\tt equalityE} theorem, 32, 71 + \item {\tt equalityI} theorem, 32, 51, 71 \item {\tt equals0D} theorem, 32 \item {\tt equals0I} theorem, 32 \item {\tt eresolve_tac}, 15 \item {\tt eta} theorem, 38, 39 - \item {\tt EX} symbol, 6, 25, 58, 60, 66, 68, 98 - \item {\tt Ex} constant, 6, 58, 98 - \item {\tt EX!} symbol, 6, 58 - \item {\tt Ex1} constant, 6, 58 - \item {\tt Ex1_def} theorem, 62 + \item {\tt EX} symbol, 6, 25, 59, 61, 68, 69, 99 + \item {\tt Ex} constant, 6, 59, 99 + \item {\tt EX!} symbol, 6, 59 + \item {\tt Ex1} constant, 6, 59 + \item {\tt Ex1_def} theorem, 63 \item {\tt ex1_def} theorem, 7 - \item {\tt ex1E} theorem, 8, 64 - \item {\tt ex1I} theorem, 8, 64 - \item {\tt Ex_def} theorem, 62 + \item {\tt ex1E} theorem, 8, 65 + \item {\tt ex1I} theorem, 8, 65 + \item {\tt Ex_def} theorem, 63 \item {\tt ex_impE} theorem, 8 - \item {\tt exCI} theorem, 10, 14, 64 - \item {\tt excluded_middle} theorem, 10, 64 - \item {\tt exE} theorem, 7, 64 - \item {\tt exI} theorem, 7, 64 - \item {\tt exL} theorem, 100 - \item {\tt expand_if} theorem, 64 - \item {\tt expand_split} theorem, 74 - \item {\tt expand_sum_case} theorem, 76 - \item {\tt exR} theorem, 100, 103, 105 - \item {\tt exR_thin} theorem, 101, 105, 106 - \item {\tt ext} theorem, 61 + \item {\tt exCI} theorem, 10, 14, 65 + \item {\tt excluded_middle} theorem, 10, 65 + \item {\tt exE} theorem, 7, 65 + \item {\tt exI} theorem, 7, 65 + \item {\tt exL} theorem, 101 + \item {\tt Exp} theory, 95 + \item {\tt expand_if} theorem, 65 + \item {\tt expand_split} theorem, 75 + \item {\tt expand_sum_case} theorem, 77 + \item {\tt exR} theorem, 101, 104, 106 + \item {\tt exR_thin} theorem, 102, 106, 107 + \item {\tt ext} theorem, 62, 63 \item {\tt extension} theorem, 29 \indexspace - \item {\tt F} constant, 110 - \item {\tt False} constant, 6, 58, 98 - \item {\tt False_def} theorem, 62 - \item {\tt FalseE} theorem, 7, 63 - \item {\tt FalseL} theorem, 100 - \item {\tt Fast_tac}, 53 - \item {\tt fast_tac}, 17, 19, 20, 54, \bold{105} - \item {\tt FE} theorem, 116, 120 - \item {\tt FEL} theorem, 116 - \item {\tt FF} theorem, 116 + \item {\tt F} constant, 111 + \item {\tt False} constant, 6, 59, 99 + \item {\tt False_def} theorem, 63 + \item {\tt FalseE} theorem, 7, 64 + \item {\tt FalseL} theorem, 101 + \item {\tt fast_tac}, \bold{106} + \item {\tt FE} theorem, 117, 121 + \item {\tt FEL} theorem, 117 + \item {\tt FF} theorem, 117 \item {\tt field} constant, 24 \item {\tt field_def} theorem, 30 \item {\tt field_subset} theorem, 37 @@ -299,9 +301,9 @@ \item {\tt fieldE} theorem, 37 \item {\tt fieldI1} theorem, 37 \item {\tt fieldI2} theorem, 37 - \item {\tt filseq_resolve_tac}, \bold{103} - \item {\tt filt_resolve_tac}, 103, 118 - \item {\tt filter} constant, 79 + \item {\tt filseq_resolve_tac}, \bold{104} + \item {\tt filt_resolve_tac}, 104, 119 + \item {\tt filter} constant, 80 \item {\tt Fin.consI} theorem, 47 \item {\tt Fin.emptyI} theorem, 47 \item {\tt Fin_induct} theorem, 47 @@ -313,30 +315,30 @@ \item {\tt Fixedpt} theory, 41 \item {\tt flat} constant, 48 \item {\tt flat_def} theorem, 48 - \item flex-flex constraints, 97 - \item {\tt FOL} theory, 1, 4, 10, 119 + \item flex-flex constraints, 98 + \item {\tt FOL} theory, 1, 4, 10, 120 \item {\tt FOL_cs}, \bold{10} \item {\tt FOL_ss}, \bold{5} - \item {\tt foldl} constant, 79 - \item {\tt form_rls}, \bold{117} - \item {\tt formL_rls}, \bold{117} - \item {\tt forms_of_seq}, \bold{102} + \item {\tt foldl} constant, 80 + \item {\tt form_rls}, \bold{118} + \item {\tt formL_rls}, \bold{118} + \item {\tt forms_of_seq}, \bold{103} \item {\tt foundation} theorem, 29 - \item {\tt fst} constant, 24, 28, 74, 110, 115 - \item {\tt fst_conv} theorem, 36, 74 - \item {\tt fst_def} theorem, 30, 115 - \item {\tt Fun} theory, 72 - \item {\tt fun} type, 59 - \item {\tt fun_cong} theorem, 63 + \item {\tt fst} constant, 24, 28, 75, 111, 116 + \item {\tt fst_conv} theorem, 36, 75 + \item {\tt fst_def} theorem, 30, 116 + \item {\tt Fun} theory, 74 + \item {\tt fun} type, 60 + \item {\tt fun_cong} theorem, 64 \item {\tt fun_disjoint_apply1} theorem, 39, 55 \item {\tt fun_disjoint_apply2} theorem, 39 - \item {\tt fun_disjoint_Un} theorem, 39, 56 + \item {\tt fun_disjoint_Un} theorem, 39, 57 \item {\tt fun_empty} theorem, 39 \item {\tt fun_extension} theorem, 38, 39 \item {\tt fun_is_rel} theorem, 38 \item {\tt fun_single} theorem, 39 \item function applications - \subitem in \CTT, 112 + \subitem in \CTT, 113 \subitem in \ZF, 24 \indexspace @@ -351,313 +353,314 @@ \indexspace - \item {\tt hd} constant, 79 - \item higher-order logic, 57--96 - \item {\tt HOL} theory, 1, 57 - \item {\sc hol} system, 57, 60 - \item {\tt HOL_cs}, \bold{73} - \item {\tt HOL_quantifiers}, \bold{60}, 68 - \item {\tt HOL_ss}, \bold{73} + \item {\tt hd} constant, 80 + \item higher-order logic, 58--97 + \item {\tt HOL} theory, 1, 58 + \item {\sc hol} system, 58, 61 + \item {\tt HOL_basic_ss}, \bold{74} + \item {\tt HOL_cs}, \bold{75} + \item {\tt HOL_quantifiers}, \bold{61}, 69 + \item {\tt HOL_ss}, \bold{74} \item {\tt HOLCF} theory, 1 - \item {\tt hyp_rew_tac}, \bold{119} - \item {\tt hyp_subst_tac}, 5 + \item {\tt hyp_rew_tac}, \bold{120} + \item {\tt hyp_subst_tac}, 5, 74 \indexspace - \item {\tt i} type, 23, 109 + \item {\tt i} type, 23, 110 \item {\tt id} constant, 44 \item {\tt id_def} theorem, 44 - \item {\tt If} constant, 58 + \item {\tt If} constant, 59 \item {\tt if} constant, 24 - \item {\tt if_def} theorem, 16, 29, 62 - \item {\tt if_not_P} theorem, 34, 64 - \item {\tt if_P} theorem, 34, 64 + \item {\tt if_def} theorem, 16, 29, 63 + \item {\tt if_not_P} theorem, 34, 65 + \item {\tt if_P} theorem, 34, 65 \item {\tt ifE} theorem, 18 - \item {\tt iff} theorem, 61 - \item {\tt iff_def} theorem, 7, 100 + \item {\tt iff} theorem, 62, 63 + \item {\tt iff_def} theorem, 7, 101 \item {\tt iff_impE} theorem, 8 - \item {\tt iffCE} theorem, 10, 64, 72 - \item {\tt iffD1} theorem, 8, 63 - \item {\tt iffD2} theorem, 8, 63 - \item {\tt iffE} theorem, 8, 63 - \item {\tt iffI} theorem, 8, 18, 63 - \item {\tt iffL} theorem, 101, 107 - \item {\tt iffR} theorem, 101 + \item {\tt iffCE} theorem, 10, 65, 69 + \item {\tt iffD1} theorem, 8, 64 + \item {\tt iffD2} theorem, 8, 64 + \item {\tt iffE} theorem, 8, 64 + \item {\tt iffI} theorem, 8, 18, 64 + \item {\tt iffL} theorem, 102, 108 + \item {\tt iffR} theorem, 102 \item {\tt ifI} theorem, 18 \item {\tt IFOL} theory, 4 \item {\tt IFOL_ss}, \bold{5} - \item {\tt image_def} theorem, 30, 68 - \item {\tt imageE} theorem, 37, 70 - \item {\tt imageI} theorem, 37, 70 + \item {\tt image_def} theorem, 30, 70 + \item {\tt imageE} theorem, 37, 72 + \item {\tt imageI} theorem, 37, 72 \item {\tt imp_impE} theorem, 8, 13 - \item {\tt impCE} theorem, 10, 64 - \item {\tt impE} theorem, 8, 9, 63 - \item {\tt impI} theorem, 7, 61 - \item {\tt impL} theorem, 100 - \item {\tt impR} theorem, 100 - \item {\tt in} symbol, 26, 59 - \item {\tt ind} type, 75 + \item {\tt impCE} theorem, 10, 65 + \item {\tt impE} theorem, 8, 9, 64 + \item {\tt impI} theorem, 7, 62 + \item {\tt impL} theorem, 101 + \item {\tt impR} theorem, 101 + \item {\tt in} symbol, 26, 60 + \item {\tt ind} type, 78 \item {\tt induct} theorem, 43 - \item {\tt induct_tac}, 77, 78, \bold{86} - \item {\tt inductive}, 90--93 + \item {\tt induct_tac}, 79, \bold{87} + \item {\tt inductive}, 91--94 \item {\tt Inf} constant, 24, 28 \item {\tt infinity} theorem, 30 - \item {\tt inj} constant, 44, 72 + \item {\tt inj} constant, 44, 74 \item {\tt inj_converse_inj} theorem, 44 - \item {\tt inj_def} theorem, 44, 72 - \item {\tt inj_Inl} theorem, 76 - \item {\tt inj_Inr} theorem, 76 - \item {\tt inj_onto} constant, 72 - \item {\tt inj_onto_def} theorem, 72 - \item {\tt inj_Suc} theorem, 76 - \item {\tt Inl} constant, 42, 76 - \item {\tt inl} constant, 110, 115, 125 + \item {\tt inj_def} theorem, 44, 74 + \item {\tt inj_Inl} theorem, 77 + \item {\tt inj_Inr} theorem, 77 + \item {\tt inj_onto} constant, 74 + \item {\tt inj_onto_def} theorem, 74 + \item {\tt inj_Suc} theorem, 77 + \item {\tt Inl} constant, 42, 77 + \item {\tt inl} constant, 111, 116, 126 \item {\tt Inl_def} theorem, 42 \item {\tt Inl_inject} theorem, 42 \item {\tt Inl_neq_Inr} theorem, 42 - \item {\tt Inl_not_Inr} theorem, 76 - \item {\tt Inr} constant, 42, 76 - \item {\tt inr} constant, 110, 115 + \item {\tt Inl_not_Inr} theorem, 77 + \item {\tt Inr} constant, 42, 77 + \item {\tt inr} constant, 111, 116 \item {\tt Inr_def} theorem, 42 \item {\tt Inr_inject} theorem, 42 - \item {\tt insert} constant, 65 - \item {\tt insert_def} theorem, 68 - \item {\tt insertE} theorem, 70 - \item {\tt insertI1} theorem, 70 - \item {\tt insertI2} theorem, 70 - \item {\tt INT} symbol, 25, 27, 65, 66, 68 - \item {\tt Int} symbol, 24, 65 - \item {\tt Int.best_tac}, \bold{9} - \item {\tt Int.fast_tac}, \bold{9}, 12 - \item {\tt Int.inst_step_tac}, \bold{9} - \item {\tt Int.safe_step_tac}, \bold{9} - \item {\tt Int.safe_tac}, \bold{9} - \item {\tt Int.step_tac}, \bold{9} - \item {\tt Int_absorb} theorem, 40, 71 - \item {\tt Int_assoc} theorem, 40, 71 - \item {\tt Int_commute} theorem, 40, 71 - \item {\tt INT_D} theorem, 70 - \item {\tt Int_def} theorem, 29, 68 - \item {\tt INT_E} theorem, 33, 70 - \item {\tt Int_greatest} theorem, 35, 51, 53, 71 - \item {\tt INT_I} theorem, 33, 70 - \item {\tt Int_Inter_image} theorem, 71 - \item {\tt Int_lower1} theorem, 35, 52, 71 - \item {\tt Int_lower2} theorem, 35, 52, 71 - \item {\tt Int_Un_distrib} theorem, 40, 71 - \item {\tt Int_Union} theorem, 71 + \item {\tt insert} constant, 67 + \item {\tt insert_def} theorem, 70 + \item {\tt insertE} theorem, 72 + \item {\tt insertI1} theorem, 72 + \item {\tt insertI2} theorem, 72 + \item {\tt INT} symbol, 25, 27, 67--69 + \item {\tt Int} symbol, 24, 67 + \item {\tt Int_absorb} theorem, 40, 73 + \item {\tt Int_assoc} theorem, 40, 73 + \item {\tt Int_commute} theorem, 40, 73 + \item {\tt INT_D} theorem, 72 + \item {\tt Int_def} theorem, 29, 70 + \item {\tt INT_E} theorem, 33, 72 + \item {\tt Int_greatest} theorem, 35, 51, 53, 73 + \item {\tt INT_I} theorem, 33, 72 + \item {\tt Int_Inter_image} theorem, 73 + \item {\tt Int_lower1} theorem, 35, 52, 73 + \item {\tt Int_lower2} theorem, 35, 52, 73 + \item {\tt Int_Un_distrib} theorem, 40, 73 + \item {\tt Int_Union} theorem, 73 \item {\tt Int_Union_RepFun} theorem, 40 - \item {\tt IntD1} theorem, 34, 70 - \item {\tt IntD2} theorem, 34, 70 - \item {\tt IntE} theorem, 34, 52, 70 - \item {\tt INTER} constant, 65 - \item {\tt Inter} constant, 24, 65 - \item {\tt INTER1} constant, 65 - \item {\tt INTER1_def} theorem, 68 - \item {\tt INTER_def} theorem, 68 - \item {\tt Inter_def} theorem, 29, 68 - \item {\tt Inter_greatest} theorem, 35, 71 - \item {\tt Inter_lower} theorem, 35, 71 - \item {\tt Inter_Un_distrib} theorem, 40, 71 - \item {\tt InterD} theorem, 33, 70 - \item {\tt InterE} theorem, 33, 70 - \item {\tt InterI} theorem, 31, 33, 70 - \item {\tt IntI} theorem, 34, 70 - \item {\tt intr_rls}, \bold{117} - \item {\tt intr_tac}, \bold{118}, 127, 128 - \item {\tt intrL_rls}, \bold{117} - \item {\tt inv} constant, 72 - \item {\tt inv_def} theorem, 72 + \item {\tt IntD1} theorem, 34, 72 + \item {\tt IntD2} theorem, 34, 72 + \item {\tt IntE} theorem, 34, 52, 72 + \item {\tt INTER} constant, 67 + \item {\tt Inter} constant, 24, 67 + \item {\tt INTER1} constant, 67 + \item {\tt INTER1_def} theorem, 70 + \item {\tt INTER_def} theorem, 70 + \item {\tt Inter_def} theorem, 29, 70 + \item {\tt Inter_greatest} theorem, 35, 73 + \item {\tt Inter_lower} theorem, 35, 73 + \item {\tt Inter_Un_distrib} theorem, 40, 73 + \item {\tt InterD} theorem, 33, 72 + \item {\tt InterE} theorem, 33, 72 + \item {\tt InterI} theorem, 31, 33, 72 + \item {\tt IntI} theorem, 34, 72 + \item {\tt IntPr.best_tac}, \bold{10} + \item {\tt IntPr.fast_tac}, \bold{9}, 12 + \item {\tt IntPr.inst_step_tac}, \bold{9} + \item {\tt IntPr.safe_step_tac}, \bold{9} + \item {\tt IntPr.safe_tac}, \bold{9} + \item {\tt IntPr.step_tac}, \bold{9} + \item {\tt intr_rls}, \bold{118} + \item {\tt intr_tac}, \bold{119}, 128, 129 + \item {\tt intrL_rls}, \bold{118} + \item {\tt inv} constant, 74 + \item {\tt inv_def} theorem, 74 \indexspace - \item {\tt lam} symbol, 25, 27, 112 + \item {\tt lam} symbol, 25, 27, 113 \item {\tt lam_def} theorem, 30 \item {\tt lam_type} theorem, 38 \item {\tt Lambda} constant, 24, 27 - \item {\tt lambda} constant, 110, 112 + \item {\tt lambda} constant, 111, 113 \item $\lambda$-abstractions - \subitem in \CTT, 112 + \subitem in \CTT, 113 \subitem in \ZF, 25 \item {\tt lamE} theorem, 38, 39 \item {\tt lamI} theorem, 38, 39 \item {\tt LCF} theory, 1 \item {\tt le_cs}, \bold{22} - \item {\tt LEAST} constant, 59, 60, 75 - \item {\tt Least} constant, 58 - \item {\tt Least_def} theorem, 62 + \item {\tt LEAST} constant, 60, 61, 78 + \item {\tt Least} constant, 59 + \item {\tt Least_def} theorem, 63 \item {\tt left_comp_id} theorem, 44 \item {\tt left_comp_inverse} theorem, 44 \item {\tt left_inverse} theorem, 44 - \item {\tt length} constant, 48, 79 + \item {\tt length} constant, 48, 80 \item {\tt length_def} theorem, 48 - \item {\tt less_induct} theorem, 77 - \item {\tt Let} constant, 23, 24, 58, 61 - \item {\tt let} symbol, 26, 59, 61 - \item {\tt Let_def} theorem, 23, 29, 61, 62 + \item {\tt less_induct} theorem, 79 + \item {\tt Let} constant, 23, 24, 59, 62 + \item {\tt let} symbol, 26, 60, 62 + \item {\tt Let_def} theorem, 23, 29, 62, 63 + \item {\tt LFilter} theory, 95 \item {\tt lfp_def} theorem, 43 \item {\tt lfp_greatest} theorem, 43 \item {\tt lfp_lowerbound} theorem, 43 \item {\tt lfp_mono} theorem, 43 \item {\tt lfp_subset} theorem, 43 \item {\tt lfp_Tarski} theorem, 43 - \item {\tt List} theory, 78, 79 + \item {\tt List} theory, 79, 80 \item {\tt list} constant, 48 - \item {\tt list} type, 78, 94 + \item {\tt list} type, 79, 95 \item {\tt List.induct} theorem, 48 - \item {\tt list_all} constant, 79 \item {\tt list_case} constant, 48 \item {\tt list_mono} theorem, 48 \item {\tt list_rec} constant, 48 \item {\tt list_rec_Cons} theorem, 48 \item {\tt list_rec_def} theorem, 48 \item {\tt list_rec_Nil} theorem, 48 - \item {\tt LK} theory, 1, 97, 101 - \item {\tt LK_dup_pack}, \bold{103}, 105 - \item {\tt LK_pack}, \bold{103} - \item {\tt LList} theory, 94 + \item {\tt LK} theory, 1, 98, 102 + \item {\tt LK_dup_pack}, \bold{104}, 106 + \item {\tt LK_pack}, \bold{104} + \item {\tt LList} theory, 95 \item {\tt logic} class, 4 \indexspace - \item {\tt map} constant, 48, 79 + \item {\tt map} constant, 48, 80 \item {\tt map_app_distrib} theorem, 48 \item {\tt map_compose} theorem, 48 \item {\tt map_def} theorem, 48 \item {\tt map_flat} theorem, 48 \item {\tt map_ident} theorem, 48 \item {\tt map_type} theorem, 48 - \item {\tt max} constant, 59, 75 - \item {\tt mem} symbol, 79 + \item {\tt max} constant, 60, 78 + \item {\tt mem} symbol, 80 \item {\tt mem_asym} theorem, 34, 35 - \item {\tt mem_Collect_eq} theorem, 68 + \item {\tt mem_Collect_eq} theorem, 69, 70 \item {\tt mem_irrefl} theorem, 34 - \item {\tt min} constant, 59, 75 - \item {\tt minus} class, 59 - \item {\tt mod} symbol, 46, 76, 121 - \item {\tt mod_def} theorem, 46, 121 - \item {\tt mod_geq} theorem, 77 - \item {\tt mod_less} theorem, 77 + \item {\tt min} constant, 60, 78 + \item {\tt minus} class, 60 + \item {\tt mod} symbol, 46, 77, 122 + \item {\tt mod_def} theorem, 46, 122 + \item {\tt mod_geq} theorem, 78 + \item {\tt mod_less} theorem, 78 \item {\tt mod_quo_equality} theorem, 46 \item {\tt Modal} theory, 1 - \item {\tt mono} constant, 59 - \item {\tt mp} theorem, 7, 61 - \item {\tt mp_tac}, \bold{9}, \bold{119} + \item {\tt mono} constant, 60 + \item {\tt mp} theorem, 7, 62 + \item {\tt mp_tac}, \bold{9}, \bold{120} \item {\tt mult_0} theorem, 46 - \item {\tt mult_assoc} theorem, 46, 121 - \item {\tt mult_commute} theorem, 46, 121 - \item {\tt mult_def} theorem, 46, 121 + \item {\tt mult_assoc} theorem, 46, 122 + \item {\tt mult_commute} theorem, 46, 122 + \item {\tt mult_def} theorem, 46, 122 \item {\tt mult_succ} theorem, 46 \item {\tt mult_type} theorem, 46 - \item {\tt mult_typing} theorem, 121 - \item {\tt multC0} theorem, 121 - \item {\tt multC_succ} theorem, 121 + \item {\tt mult_typing} theorem, 122 + \item {\tt multC0} theorem, 122 + \item {\tt multC_succ} theorem, 122 \indexspace - \item {\tt N} constant, 110 - \item {\tt n_not_Suc_n} theorem, 76 - \item {\tt Nat} theory, 45, 75 + \item {\tt N} constant, 111 + \item {\tt n_not_Suc_n} theorem, 77 + \item {\tt Nat} theory, 45, 78 \item {\tt nat} constant, 46 - \item {\tt nat} type, 75 + \item {\tt nat} type, 78 \item {\tt nat_0I} theorem, 46 \item {\tt nat_case} constant, 46 \item {\tt nat_case_0} theorem, 46 \item {\tt nat_case_def} theorem, 46 \item {\tt nat_case_succ} theorem, 46 \item {\tt nat_def} theorem, 46 - \item {\tt nat_induct} theorem, 46, 76 - \item {\tt nat_rec} constant, 77 + \item {\tt nat_induct} theorem, 46, 77 + \item {\tt nat_rec} constant, 79 \item {\tt nat_succI} theorem, 46 - \item {\tt NatDef} theory, 75 - \item {\tt NC0} theorem, 114 - \item {\tt NC_succ} theorem, 114 - \item {\tt NE} theorem, 113, 114, 122 - \item {\tt NEL} theorem, 114 - \item {\tt NF} theorem, 114, 123 - \item {\tt NI0} theorem, 114 - \item {\tt NI_succ} theorem, 114 - \item {\tt NI_succL} theorem, 114 + \item {\tt NatDef} theory, 78 + \item {\tt NC0} theorem, 115 + \item {\tt NC_succ} theorem, 115 + \item {\tt NE} theorem, 114, 115, 123 + \item {\tt NEL} theorem, 115 + \item {\tt NF} theorem, 115, 124 + \item {\tt NI0} theorem, 115 + \item {\tt NI_succ} theorem, 115 + \item {\tt NI_succL} theorem, 115 \item {\tt Nil_Cons_iff} theorem, 48 \item {\tt NilI} theorem, 48 - \item {\tt NIO} theorem, 122 - \item {\tt Not} constant, 6, 58, 98 - \item {\tt not_def} theorem, 7, 41, 62 + \item {\tt NIO} theorem, 123 + \item {\tt Not} constant, 6, 59, 99 + \item {\tt not_def} theorem, 7, 41, 63 \item {\tt not_impE} theorem, 8 - \item {\tt not_sym} theorem, 63 - \item {\tt notE} theorem, 8, 9, 63 - \item {\tt notI} theorem, 8, 63 - \item {\tt notL} theorem, 100 - \item {\tt notnotD} theorem, 10, 64 - \item {\tt notR} theorem, 100 - \item {\tt nth} constant, 79 - \item {\tt null} constant, 79 + \item {\tt not_sym} theorem, 64 + \item {\tt notE} theorem, 8, 9, 64 + \item {\tt notI} theorem, 8, 64 + \item {\tt notL} theorem, 101 + \item {\tt notnotD} theorem, 10, 65 + \item {\tt notR} theorem, 101 + \item {\tt nth} constant, 80 + \item {\tt null} constant, 80 \indexspace \item {\tt O} symbol, 44 - \item {\tt o} symbol, 58, 72 - \item {\tt o} type, 4, 97 - \item {\tt o_def} theorem, 62 - \item {\tt of} symbol, 61 - \item {\tt or_def} theorem, 41, 62 - \item {\tt Ord} theory, 59 - \item {\tt ord} class, 59, 60, 75 - \item {\tt order} class, 59 + \item {\tt o} symbol, 59, 70 + \item {\tt o} type, 4, 98 + \item {\tt o_def} theorem, 63 + \item {\tt of} symbol, 62 + \item {\tt or_def} theorem, 41, 63 + \item {\tt Ord} theory, 60 + \item {\tt ord} class, 60, 61, 78 + \item {\tt order} class, 60 \indexspace - \item {\tt pack} ML type, 103 - \item {\tt Pair} constant, 24, 25, 74 - \item {\tt pair} constant, 110 + \item {\tt pack} ML type, 104 + \item {\tt Pair} constant, 24, 25, 75 + \item {\tt pair} constant, 111 \item {\tt Pair_def} theorem, 30 - \item {\tt Pair_eq} theorem, 74 - \item {\tt Pair_inject} theorem, 36, 74 + \item {\tt Pair_eq} theorem, 75 + \item {\tt Pair_inject} theorem, 36, 75 \item {\tt Pair_inject1} theorem, 36 \item {\tt Pair_inject2} theorem, 36 \item {\tt Pair_neq_0} theorem, 36 - \item {\tt PairE} theorem, 74 + \item {\tt PairE} theorem, 75 \item {\tt pairing} theorem, 33 - \item {\tt pc_tac}, \bold{104}, \bold{120}, 126, 127 + \item {\tt pc_tac}, \bold{105}, \bold{121}, 127, 128 \item {\tt Perm} theory, 41 \item {\tt Pi} constant, 24, 27, 39 \item {\tt Pi_def} theorem, 30 \item {\tt Pi_type} theorem, 38, 39 - \item {\tt plus} class, 59 - \item {\tt PlusC_inl} theorem, 116 - \item {\tt PlusC_inr} theorem, 116 - \item {\tt PlusE} theorem, 116, 120, 124 - \item {\tt PlusEL} theorem, 116 - \item {\tt PlusF} theorem, 116 - \item {\tt PlusFL} theorem, 116 - \item {\tt PlusI_inl} theorem, 116, 125 - \item {\tt PlusI_inlL} theorem, 116 - \item {\tt PlusI_inr} theorem, 116 - \item {\tt PlusI_inrL} theorem, 116 - \item {\tt Pow} constant, 24, 65 - \item {\tt Pow_def} theorem, 68 + \item {\tt plus} class, 60 + \item {\tt PlusC_inl} theorem, 117 + \item {\tt PlusC_inr} theorem, 117 + \item {\tt PlusE} theorem, 117, 121, 125 + \item {\tt PlusEL} theorem, 117 + \item {\tt PlusF} theorem, 117 + \item {\tt PlusFL} theorem, 117 + \item {\tt PlusI_inl} theorem, 117, 126 + \item {\tt PlusI_inlL} theorem, 117 + \item {\tt PlusI_inr} theorem, 117 + \item {\tt PlusI_inrL} theorem, 117 + \item {\tt Pow} constant, 24, 67 + \item {\tt Pow_def} theorem, 70 \item {\tt Pow_iff} theorem, 29 \item {\tt Pow_mono} theorem, 51 - \item {\tt PowD} theorem, 32, 52, 70 - \item {\tt PowI} theorem, 32, 52, 70 - \item primitive recursion, 88--90 - \item {\tt primrec}, 88--90 - \item {\tt primrec} symbol, 77 + \item {\tt PowD} theorem, 32, 52, 72 + \item {\tt PowI} theorem, 32, 52, 72 + \item primitive recursion, 89--91 + \item {\tt primrec}, 89--91 + \item {\tt primrec} symbol, 78 \item {\tt PrimReplace} constant, 24, 28 \item priorities, 2 - \item {\tt PROD} symbol, 25, 27, 111, 112 - \item {\tt Prod} constant, 110 - \item {\tt Prod} theory, 74 - \item {\tt ProdC} theorem, 114, 130 - \item {\tt ProdC2} theorem, 114 - \item {\tt ProdE} theorem, 114, 127, 129, 131 - \item {\tt ProdEL} theorem, 114 - \item {\tt ProdF} theorem, 114 - \item {\tt ProdFL} theorem, 114 - \item {\tt ProdI} theorem, 114, 120, 122 - \item {\tt ProdIL} theorem, 114 - \item {\tt prop_cs}, \bold{10}, \bold{73} - \item {\tt prop_pack}, \bold{103} + \item {\tt PROD} symbol, 25, 27, 112, 113 + \item {\tt Prod} constant, 111 + \item {\tt Prod} theory, 75 + \item {\tt ProdC} theorem, 115, 131 + \item {\tt ProdC2} theorem, 115 + \item {\tt ProdE} theorem, 115, 128, 130, 132 + \item {\tt ProdEL} theorem, 115 + \item {\tt ProdF} theorem, 115 + \item {\tt ProdFL} theorem, 115 + \item {\tt ProdI} theorem, 115, 121, 123 + \item {\tt ProdIL} theorem, 115 + \item {\tt prop_cs}, \bold{10}, \bold{75} + \item {\tt prop_pack}, \bold{104} \indexspace @@ -678,112 +681,113 @@ \indexspace - \item {\tt range} constant, 24, 65, 95 - \item {\tt range_def} theorem, 30, 68 + \item {\tt range} constant, 24, 67, 96 + \item {\tt range_def} theorem, 30, 70 \item {\tt range_of_fun} theorem, 38, 39 \item {\tt range_subset} theorem, 37 \item {\tt range_type} theorem, 38 - \item {\tt rangeE} theorem, 37, 70, 95 - \item {\tt rangeI} theorem, 37, 70 + \item {\tt rangeE} theorem, 37, 72, 96 + \item {\tt rangeI} theorem, 37, 72 \item {\tt rank} constant, 47 \item {\tt rank_ss}, \bold{22} - \item {\tt rec} constant, 46, 110, 113 + \item {\tt rec} constant, 46, 111, 114 \item {\tt rec_0} theorem, 46 \item {\tt rec_def} theorem, 46 \item {\tt rec_succ} theorem, 46 - \item {\tt red_if_equal} theorem, 113 - \item {\tt Reduce} constant, 110, 113, 119 - \item {\tt refl} theorem, 7, 61, 100 - \item {\tt refl_elem} theorem, 113, 117 - \item {\tt refl_red} theorem, 113 - \item {\tt refl_type} theorem, 113, 117 - \item {\tt REPEAT_FIRST}, 118 - \item {\tt repeat_goal_tac}, \bold{104} + \item {\tt red_if_equal} theorem, 114 + \item {\tt Reduce} constant, 111, 114, 120 + \item {\tt refl} theorem, 7, 62, 101 + \item {\tt refl_elem} theorem, 114, 118 + \item {\tt refl_red} theorem, 114 + \item {\tt refl_type} theorem, 114, 118 + \item {\tt REPEAT_FIRST}, 119 + \item {\tt repeat_goal_tac}, \bold{105} \item {\tt RepFun} constant, 24, 27, 28, 31 \item {\tt RepFun_def} theorem, 29 \item {\tt RepFunE} theorem, 33 \item {\tt RepFunI} theorem, 33 \item {\tt Replace} constant, 24, 27, 28, 31 \item {\tt Replace_def} theorem, 29 - \item {\tt replace_type} theorem, 117, 129 + \item {\tt replace_type} theorem, 118, 130 \item {\tt ReplaceE} theorem, 33 \item {\tt ReplaceI} theorem, 33 \item {\tt replacement} theorem, 29 - \item {\tt reresolve_tac}, \bold{104} - \item {\tt res_inst_tac}, 60 + \item {\tt reresolve_tac}, \bold{105} + \item {\tt res_inst_tac}, 61 \item {\tt restrict} constant, 24, 31 \item {\tt restrict} theorem, 38 \item {\tt restrict_bij} theorem, 44 \item {\tt restrict_def} theorem, 30 \item {\tt restrict_type} theorem, 38 - \item {\tt rev} constant, 48, 79 + \item {\tt rev} constant, 48, 80 \item {\tt rev_def} theorem, 48 - \item {\tt rew_tac}, 17, \bold{119} + \item {\tt rew_tac}, 17, \bold{120} \item {\tt rewrite_rule}, 18 \item {\tt right_comp_id} theorem, 44 \item {\tt right_comp_inverse} theorem, 44 \item {\tt right_inverse} theorem, 44 - \item {\tt RL}, 124 - \item {\tt RS}, 129, 131 + \item {\tt RL}, 125 + \item {\tt RS}, 130, 132 \indexspace - \item {\tt safe_goal_tac}, \bold{105} - \item {\tt safe_tac}, \bold{120} - \item {\tt safestep_tac}, \bold{120} + \item {\tt safe_goal_tac}, \bold{106} + \item {\tt safe_tac}, \bold{121} + \item {\tt safestep_tac}, \bold{121} \item search - \subitem best-first, 96 - \item {\tt select_equality} theorem, 61, 64 - \item {\tt selectI} theorem, 61 + \subitem best-first, 97 + \item {\tt select_equality} theorem, 63, 65 + \item {\tt selectI} theorem, 62, 63 \item {\tt separation} theorem, 33 - \item {\tt Seqof} constant, 98 - \item sequent calculus, 97--108 - \item {\tt Set} theory, 67, 68 - \item {\tt set} type, 67 - \item set theory, 22--56 - \item {\tt set_current_thy}, 96 - \item {\tt set_diff_def} theorem, 68 - \item {\tt set_of_list} constant, 79 - \item {\tt show_sorts}, 60 - \item {\tt show_types}, 60 - \item {\tt Sigma} constant, 24, 27, 28, 36, 74 - \item {\tt Sigma_def} theorem, 30, 74 - \item {\tt SigmaE} theorem, 36, 74 + \item {\tt Seqof} constant, 99 + \item sequent calculus, 98--109 + \item {\tt Set} theory, 66, 69 + \item {\tt set} type, 66 + \item set theory, 22--57 + \item {\tt set_current_thy}, 97 + \item {\tt set_diff_def} theorem, 70 + \item {\tt set_of_list} constant, 80 + \item {\tt show_sorts}, 61 + \item {\tt show_types}, 61 + \item {\tt Sigma} constant, 24, 27, 28, 36, 75 + \item {\tt Sigma_def} theorem, 30, 75 + \item {\tt SigmaE} theorem, 36, 75 \item {\tt SigmaE2} theorem, 36 - \item {\tt SigmaI} theorem, 36, 74 + \item {\tt SigmaI} theorem, 36, 75 \item simplification - \subitem of conjunctions, 73 + \subitem of conjunctions, 5, 74 \item {\tt singletonE} theorem, 34 \item {\tt singletonI} theorem, 34 - \item {\tt snd} constant, 24, 28, 74, 110, 115 - \item {\tt snd_conv} theorem, 36, 74 - \item {\tt snd_def} theorem, 30, 115 - \item {\tt sobj} type, 99 - \item {\tt spec} theorem, 7, 64 - \item {\tt split} constant, 24, 28, 74, 110, 124 - \item {\tt split} theorem, 36, 74 - \item {\tt split_all_tac}, \bold{75} + \item {\tt snd} constant, 24, 28, 75, 111, 116 + \item {\tt snd_conv} theorem, 36, 75 + \item {\tt snd_def} theorem, 30, 116 + \item {\tt sobj} type, 100 + \item {\tt spec} theorem, 7, 65 + \item {\tt split} constant, 24, 28, 75, 111, 125 + \item {\tt split} theorem, 36, 75 + \item {\tt split_all_tac}, \bold{76} \item {\tt split_def} theorem, 30 - \item {\tt ssubst} theorem, 8, 62, 63 - \item {\tt stac}, \bold{73} - \item {\tt step_tac}, 21, \bold{105}, \bold{120} - \item {\tt strip_tac}, \bold{62} - \item {\tt subset_def} theorem, 29, 68 - \item {\tt subset_refl} theorem, 32, 69 - \item {\tt subset_trans} theorem, 32, 69 - \item {\tt subsetCE} theorem, 32, 69, 72 - \item {\tt subsetD} theorem, 32, 54, 69, 72 - \item {\tt subsetI} theorem, 32, 52, 53, 69 - \item {\tt subst} theorem, 7, 61 - \item {\tt subst_elem} theorem, 113 - \item {\tt subst_elemL} theorem, 113 - \item {\tt subst_eqtyparg} theorem, 117, 129 - \item {\tt subst_prodE} theorem, 115, 117 - \item {\tt subst_type} theorem, 113 - \item {\tt subst_typeL} theorem, 113 - \item {\tt Suc} constant, 76 - \item {\tt Suc_not_Zero} theorem, 76 - \item {\tt succ} constant, 24, 28, 110 + \item {\tt ssubst} theorem, 8, 64, 66 + \item {\tt stac}, \bold{74} + \item {\tt Step_tac}, 21 + \item {\tt step_tac}, 21, \bold{106}, \bold{121} + \item {\tt strip_tac}, \bold{66} + \item {\tt subset_def} theorem, 29, 70 + \item {\tt subset_refl} theorem, 32, 71 + \item {\tt subset_trans} theorem, 32, 71 + \item {\tt subsetCE} theorem, 32, 69, 71 + \item {\tt subsetD} theorem, 32, 54, 69, 71 + \item {\tt subsetI} theorem, 32, 52, 53, 71 + \item {\tt subst} theorem, 7, 62 + \item {\tt subst_elem} theorem, 114 + \item {\tt subst_elemL} theorem, 114 + \item {\tt subst_eqtyparg} theorem, 118, 130 + \item {\tt subst_prodE} theorem, 116, 118 + \item {\tt subst_type} theorem, 114 + \item {\tt subst_typeL} theorem, 114 + \item {\tt Suc} constant, 77 + \item {\tt Suc_not_Zero} theorem, 77 + \item {\tt succ} constant, 24, 28, 111 \item {\tt succ_def} theorem, 30 \item {\tt succ_inject} theorem, 34 \item {\tt succ_neq_0} theorem, 34 @@ -791,12 +795,12 @@ \item {\tt succE} theorem, 34 \item {\tt succI1} theorem, 34 \item {\tt succI2} theorem, 34 - \item {\tt SUM} symbol, 25, 27, 111, 112 - \item {\tt Sum} constant, 110 - \item {\tt Sum} theory, 41, 75 - \item {\tt sum_case} constant, 76 - \item {\tt sum_case_Inl} theorem, 76 - \item {\tt sum_case_Inr} theorem, 76 + \item {\tt SUM} symbol, 25, 27, 112, 113 + \item {\tt Sum} constant, 111 + \item {\tt Sum} theory, 41, 76 + \item {\tt sum_case} constant, 77 + \item {\tt sum_case_Inl} theorem, 77 + \item {\tt sum_case_Inr} theorem, 77 \item {\tt sum_def} theorem, 42 \item {\tt sum_InlI} theorem, 42 \item {\tt sum_InrI} theorem, 42 @@ -804,110 +808,111 @@ \item {\tt SUM_Int_distrib2} theorem, 40 \item {\tt SUM_Un_distrib1} theorem, 40 \item {\tt SUM_Un_distrib2} theorem, 40 - \item {\tt SumC} theorem, 115 - \item {\tt SumE} theorem, 115, 120, 124 - \item {\tt sumE} theorem, 76 + \item {\tt SumC} theorem, 116 + \item {\tt SumE} theorem, 116, 121, 125 + \item {\tt sumE} theorem, 77 \item {\tt sumE2} theorem, 42 - \item {\tt SumE_fst} theorem, 115, 117, 129, 130 - \item {\tt SumE_snd} theorem, 115, 117, 131 - \item {\tt SumEL} theorem, 115 - \item {\tt SumF} theorem, 115 - \item {\tt SumFL} theorem, 115 - \item {\tt SumI} theorem, 115, 125 - \item {\tt SumIL} theorem, 115 - \item {\tt SumIL2} theorem, 117 - \item {\tt surj} constant, 44, 72 - \item {\tt surj_def} theorem, 44, 72 - \item {\tt surjective_pairing} theorem, 74 - \item {\tt surjective_sum} theorem, 76 - \item {\tt swap} theorem, 10, 64 - \item {\tt swap_res_tac}, 15, 96 - \item {\tt sym} theorem, 8, 63, 100 - \item {\tt sym_elem} theorem, 113 - \item {\tt sym_type} theorem, 113 - \item {\tt symL} theorem, 101 + \item {\tt SumE_fst} theorem, 116, 118, 130, 131 + \item {\tt SumE_snd} theorem, 116, 118, 132 + \item {\tt SumEL} theorem, 116 + \item {\tt SumF} theorem, 116 + \item {\tt SumFL} theorem, 116 + \item {\tt SumI} theorem, 116, 126 + \item {\tt SumIL} theorem, 116 + \item {\tt SumIL2} theorem, 118 + \item {\tt surj} constant, 44, 70, 74 + \item {\tt surj_def} theorem, 44, 74 + \item {\tt surjective_pairing} theorem, 75 + \item {\tt surjective_sum} theorem, 77 + \item {\tt swap} theorem, 10, 65 + \item {\tt swap_res_tac}, 15, 97 + \item {\tt sym} theorem, 8, 64, 101 + \item {\tt sym_elem} theorem, 114 + \item {\tt sym_type} theorem, 114 + \item {\tt symL} theorem, 102 \indexspace - \item {\tt T} constant, 110 - \item {\tt t} type, 109 - \item {\tt take} constant, 79 - \item {\tt takeWhile} constant, 79 - \item {\tt TC} theorem, 116 - \item {\tt TE} theorem, 116 - \item {\tt TEL} theorem, 116 - \item {\tt term} class, 4, 59, 97 - \item {\tt test_assume_tac}, \bold{118} - \item {\tt TF} theorem, 116 - \item {\tt THE} symbol, 25, 27, 35, 98 - \item {\tt The} constant, 24, 27, 28, 98 - \item {\tt The} theorem, 100 + \item {\tt T} constant, 111 + \item {\tt t} type, 110 + \item {\tt take} constant, 80 + \item {\tt takeWhile} constant, 80 + \item {\tt TC} theorem, 117 + \item {\tt TE} theorem, 117 + \item {\tt TEL} theorem, 117 + \item {\tt term} class, 4, 60, 98 + \item {\tt test_assume_tac}, \bold{119} + \item {\tt TF} theorem, 117 + \item {\tt THE} symbol, 25, 27, 35, 99 + \item {\tt The} constant, 24, 27, 28, 99 + \item {\tt The} theorem, 101 \item {\tt the_def} theorem, 29 \item {\tt the_equality} theorem, 34, 35 \item {\tt theI} theorem, 34, 35 - \item {\tt thinL} theorem, 100 - \item {\tt thinR} theorem, 100 - \item {\tt TI} theorem, 116 - \item {\tt times} class, 59 - \item {\tt tl} constant, 79 + \item {\tt thinL} theorem, 101 + \item {\tt thinR} theorem, 101 + \item {\tt TI} theorem, 117 + \item {\tt times} class, 60 + \item {\tt tl} constant, 80 \item tracing - \subitem of unification, 60 - \item {\tt trans} theorem, 8, 63, 100 - \item {\tt trans_elem} theorem, 113 - \item {\tt trans_red} theorem, 113 - \item {\tt trans_tac}, 77 - \item {\tt trans_type} theorem, 113 - \item {\tt True} constant, 6, 58, 98 - \item {\tt True_def} theorem, 7, 62, 100 - \item {\tt True_or_False} theorem, 61 - \item {\tt TrueI} theorem, 8, 63 - \item {\tt Trueprop} constant, 6, 58, 98 - \item {\tt TrueR} theorem, 101 - \item {\tt tt} constant, 110 - \item {\tt ttl} constant, 79 - \item {\tt Type} constant, 110 - \item type definition, \bold{78} - \item {\tt typechk_tac}, \bold{118}, 123, 126, 130, 131 + \subitem of unification, 61 + \item {\tt trans} theorem, 8, 64, 101 + \item {\tt trans_elem} theorem, 114 + \item {\tt trans_red} theorem, 114 + \item {\tt trans_tac}, 79 + \item {\tt trans_type} theorem, 114 + \item {\tt True} constant, 6, 59, 99 + \item {\tt True_def} theorem, 7, 63, 101 + \item {\tt True_or_False} theorem, 62, 63 + \item {\tt TrueI} theorem, 8, 64 + \item {\tt Trueprop} constant, 6, 59, 99 + \item {\tt TrueR} theorem, 102 + \item {\tt tt} constant, 111 + \item {\tt ttl} constant, 80 + \item {\tt Type} constant, 111 + \item type definition, \bold{82} + \item {\tt typechk_tac}, \bold{119}, 124, 127, 131, 132 + \item {\tt typedef}, 79 \indexspace - \item {\tt UN} symbol, 25, 27, 65, 66, 68 - \item {\tt Un} symbol, 24, 65 - \item {\tt Un1} theorem, 72 - \item {\tt Un2} theorem, 72 - \item {\tt Un_absorb} theorem, 40, 71 - \item {\tt Un_assoc} theorem, 40, 71 - \item {\tt Un_commute} theorem, 40, 71 - \item {\tt Un_def} theorem, 29, 68 - \item {\tt UN_E} theorem, 33, 70 - \item {\tt UN_I} theorem, 33, 70 - \item {\tt Un_Int_distrib} theorem, 40, 71 - \item {\tt Un_Inter} theorem, 71 + \item {\tt UN} symbol, 25, 27, 67--69 + \item {\tt Un} symbol, 24, 67 + \item {\tt Un1} theorem, 69 + \item {\tt Un2} theorem, 69 + \item {\tt Un_absorb} theorem, 40, 73 + \item {\tt Un_assoc} theorem, 40, 73 + \item {\tt Un_commute} theorem, 40, 73 + \item {\tt Un_def} theorem, 29, 70 + \item {\tt UN_E} theorem, 33, 72 + \item {\tt UN_I} theorem, 33, 72 + \item {\tt Un_Int_distrib} theorem, 40, 73 + \item {\tt Un_Inter} theorem, 73 \item {\tt Un_Inter_RepFun} theorem, 40 - \item {\tt Un_least} theorem, 35, 71 - \item {\tt Un_Union_image} theorem, 71 - \item {\tt Un_upper1} theorem, 35, 71 - \item {\tt Un_upper2} theorem, 35, 71 - \item {\tt UnCI} theorem, 34, 35, 70, 72 - \item {\tt UnE} theorem, 34, 70 - \item {\tt UnI1} theorem, 34, 35, 55, 70 - \item {\tt UnI2} theorem, 34, 35, 70 + \item {\tt Un_least} theorem, 35, 73 + \item {\tt Un_Union_image} theorem, 73 + \item {\tt Un_upper1} theorem, 35, 73 + \item {\tt Un_upper2} theorem, 35, 73 + \item {\tt UnCI} theorem, 34, 35, 69, 72 + \item {\tt UnE} theorem, 34, 72 + \item {\tt UnI1} theorem, 34, 35, 56, 72 + \item {\tt UnI2} theorem, 34, 35, 72 \item unification - \subitem incompleteness of, 60 - \item {\tt Unify.trace_types}, 60 - \item {\tt UNION} constant, 65 - \item {\tt Union} constant, 24, 65 - \item {\tt UNION1} constant, 65 - \item {\tt UNION1_def} theorem, 68 - \item {\tt UNION_def} theorem, 68 - \item {\tt Union_def} theorem, 68 + \subitem incompleteness of, 61 + \item {\tt Unify.trace_types}, 61 + \item {\tt UNION} constant, 67 + \item {\tt Union} constant, 24, 67 + \item {\tt UNION1} constant, 67 + \item {\tt UNION1_def} theorem, 70 + \item {\tt UNION_def} theorem, 70 + \item {\tt Union_def} theorem, 70 \item {\tt Union_iff} theorem, 29 - \item {\tt Union_least} theorem, 35, 71 - \item {\tt Union_Un_distrib} theorem, 40, 71 - \item {\tt Union_upper} theorem, 35, 71 - \item {\tt UnionE} theorem, 33, 54, 70 - \item {\tt UnionI} theorem, 33, 54, 70 - \item {\tt unit_eq} theorem, 75 + \item {\tt Union_least} theorem, 35, 73 + \item {\tt Union_Un_distrib} theorem, 40, 73 + \item {\tt Union_upper} theorem, 35, 73 + \item {\tt UnionE} theorem, 33, 54, 72 + \item {\tt UnionI} theorem, 33, 54, 72 + \item {\tt unit_eq} theorem, 76 \item {\tt Univ} theory, 45 \item {\tt Upair} constant, 23, 24, 28 \item {\tt Upair_def} theorem, 29 @@ -923,7 +928,7 @@ \indexspace - \item {\tt when} constant, 110, 115, 124 + \item {\tt when} constant, 111, 116, 125 \indexspace @@ -931,8 +936,8 @@ \indexspace - \item {\tt zero_ne_succ} theorem, 113, 114 - \item {\tt ZF} theory, 1, 22, 57 + \item {\tt zero_ne_succ} theorem, 114, 115 + \item {\tt ZF} theory, 1, 22, 58 \item {\tt ZF_cs}, \bold{22} \item {\tt ZF_ss}, \bold{22} diff -r 434b33c5f827 -r a8faa68c68b5 doc-src/Logics/logics.rao --- a/doc-src/Logics/logics.rao Fri May 09 19:41:46 1997 +0200 +++ b/doc-src/Logics/logics.rao Fri May 09 19:42:09 1997 +0200 @@ -1,12 +1,12 @@ -% This file was generated by '/usr/stud/berghofe/latex/rail/rail' from 'logics.rai' -\rail@i {1}{ typedef : 'typedef' ( () | '(' tname ')') type '=' set witness; type : typevarlist name ( () | '(' infix ')' ); tname : name; set : string; witness : () | '(' id ')'; } +% This file was generated by 'rail' from 'logics.rai' +\rail@i {1}{ typedef : 'typedef' ( () | '(' name ')') type '=' set witness; type : typevarlist name ( () | '(' infix ')' ); set : string; witness : () | '(' id ')'; } \rail@o {1}{ \rail@begin{2}{typedef} \rail@term{typedef}[] \rail@bar \rail@nextbar{1} \rail@term{(}[] -\rail@nont{tname}[] +\rail@nont{name}[] \rail@term{)}[] \rail@endbar \rail@nont{type}[] @@ -24,9 +24,6 @@ \rail@term{)}[] \rail@endbar \rail@end -\rail@begin{1}{tname} -\rail@nont{name}[] -\rail@end \rail@begin{1}{set} \rail@nont{string}[] \rail@end