src/HOL/UNITY/UNITY_tactics.ML
author paulson
Thu Jan 30 10:35:56 2003 +0100 (2003-01-30)
changeset 13796 19f50fa807ae
parent 13792 d1811693899c
child 13797 baefae13ad37
permissions -rw-r--r--
converting more UNITY theories to new-style
     1 (*  Title:      HOL/UNITY/UNITY_tactics.ML
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   2003  University of Cambridge
     5 
     6 Specialized UNITY tactics, and ML bindings of theorems
     7 *)
     8 
     9 (*FP*)
    10 val stable_FP_Orig_Int = thm "stable_FP_Orig_Int";
    11 val FP_Orig_weakest = thm "FP_Orig_weakest";
    12 val stable_FP_Int = thm "stable_FP_Int";
    13 val FP_equivalence = thm "FP_equivalence";
    14 val FP_weakest = thm "FP_weakest";
    15 val Compl_FP = thm "Compl_FP";
    16 val Diff_FP = thm "Diff_FP";
    17 
    18 (*SubstAx*)
    19 val LeadsTo_eq_leadsTo = thm "LeadsTo_eq_leadsTo";
    20 val Always_LeadsTo_pre = thm "Always_LeadsTo_pre";
    21 val Always_LeadsTo_post = thm "Always_LeadsTo_post";
    22 val Always_LeadsToI = thm "Always_LeadsToI";
    23 val Always_LeadsToD = thm "Always_LeadsToD";
    24 val leadsTo_imp_LeadsTo = thm "leadsTo_imp_LeadsTo";
    25 val LeadsTo_Trans = thm "LeadsTo_Trans";
    26 val LeadsTo_Union = thm "LeadsTo_Union";
    27 val LeadsTo_UNIV = thm "LeadsTo_UNIV";
    28 val LeadsTo_Un_duplicate = thm "LeadsTo_Un_duplicate";
    29 val LeadsTo_Un_duplicate2 = thm "LeadsTo_Un_duplicate2";
    30 val LeadsTo_UN = thm "LeadsTo_UN";
    31 val LeadsTo_Un = thm "LeadsTo_Un";
    32 val single_LeadsTo_I = thm "single_LeadsTo_I";
    33 val subset_imp_LeadsTo = thm "subset_imp_LeadsTo";
    34 val empty_LeadsTo = thm "empty_LeadsTo";
    35 val LeadsTo_weaken_R = thm "LeadsTo_weaken_R";
    36 val LeadsTo_weaken_L = thm "LeadsTo_weaken_L";
    37 val LeadsTo_weaken = thm "LeadsTo_weaken";
    38 val Always_LeadsTo_weaken = thm "Always_LeadsTo_weaken";
    39 val LeadsTo_Un_post = thm "LeadsTo_Un_post";
    40 val LeadsTo_Trans_Un = thm "LeadsTo_Trans_Un";
    41 val LeadsTo_Un_distrib = thm "LeadsTo_Un_distrib";
    42 val LeadsTo_UN_distrib = thm "LeadsTo_UN_distrib";
    43 val LeadsTo_Union_distrib = thm "LeadsTo_Union_distrib";
    44 val LeadsTo_Basis = thm "LeadsTo_Basis";
    45 val EnsuresI = thm "EnsuresI";
    46 val Always_LeadsTo_Basis = thm "Always_LeadsTo_Basis";
    47 val LeadsTo_Diff = thm "LeadsTo_Diff";
    48 val LeadsTo_UN_UN = thm "LeadsTo_UN_UN";
    49 val LeadsTo_UN_UN_noindex = thm "LeadsTo_UN_UN_noindex";
    50 val all_LeadsTo_UN_UN = thm "all_LeadsTo_UN_UN";
    51 val LeadsTo_Un_Un = thm "LeadsTo_Un_Un";
    52 val LeadsTo_cancel2 = thm "LeadsTo_cancel2";
    53 val LeadsTo_cancel_Diff2 = thm "LeadsTo_cancel_Diff2";
    54 val LeadsTo_cancel1 = thm "LeadsTo_cancel1";
    55 val LeadsTo_cancel_Diff1 = thm "LeadsTo_cancel_Diff1";
    56 val LeadsTo_empty = thm "LeadsTo_empty";
    57 val PSP_Stable = thm "PSP_Stable";
    58 val PSP_Stable2 = thm "PSP_Stable2";
    59 val PSP = thm "PSP";
    60 val PSP2 = thm "PSP2";
    61 val PSP_Unless = thm "PSP_Unless";
    62 val Stable_transient_Always_LeadsTo = thm "Stable_transient_Always_LeadsTo";
    63 val LeadsTo_wf_induct = thm "LeadsTo_wf_induct";
    64 val Bounded_induct = thm "Bounded_induct";
    65 val LessThan_induct = thm "LessThan_induct";
    66 val integ_0_le_induct = thm "integ_0_le_induct";
    67 val LessThan_bounded_induct = thm "LessThan_bounded_induct";
    68 val GreaterThan_bounded_induct = thm "GreaterThan_bounded_induct";
    69 val Completion = thm "Completion";
    70 val Finite_completion_lemma = thm "Finite_completion_lemma";
    71 val Finite_completion = thm "Finite_completion";
    72 val Stable_completion = thm "Stable_completion";
    73 val Finite_stable_completion = thm "Finite_stable_completion";
    74 
    75 (*Union*)
    76 val Init_SKIP = thm "Init_SKIP";
    77 val Acts_SKIP = thm "Acts_SKIP";
    78 val AllowedActs_SKIP = thm "AllowedActs_SKIP";
    79 val reachable_SKIP = thm "reachable_SKIP";
    80 val SKIP_in_constrains_iff = thm "SKIP_in_constrains_iff";
    81 val SKIP_in_Constrains_iff = thm "SKIP_in_Constrains_iff";
    82 val SKIP_in_stable = thm "SKIP_in_stable";
    83 val Init_Join = thm "Init_Join";
    84 val Acts_Join = thm "Acts_Join";
    85 val AllowedActs_Join = thm "AllowedActs_Join";
    86 val JN_empty = thm "JN_empty";
    87 val JN_insert = thm "JN_insert";
    88 val Init_JN = thm "Init_JN";
    89 val Acts_JN = thm "Acts_JN";
    90 val AllowedActs_JN = thm "AllowedActs_JN";
    91 val JN_cong = thm "JN_cong";
    92 val Join_commute = thm "Join_commute";
    93 val Join_assoc = thm "Join_assoc";
    94 val Join_left_commute = thm "Join_left_commute";
    95 val Join_SKIP_left = thm "Join_SKIP_left";
    96 val Join_SKIP_right = thm "Join_SKIP_right";
    97 val Join_absorb = thm "Join_absorb";
    98 val Join_left_absorb = thm "Join_left_absorb";
    99 val Join_ac = thms "Join_ac";
   100 val JN_absorb = thm "JN_absorb";
   101 val JN_Un = thm "JN_Un";
   102 val JN_constant = thm "JN_constant";
   103 val JN_Join_distrib = thm "JN_Join_distrib";
   104 val JN_Join_miniscope = thm "JN_Join_miniscope";
   105 val JN_Join_diff = thm "JN_Join_diff";
   106 val JN_constrains = thm "JN_constrains";
   107 val Join_constrains = thm "Join_constrains";
   108 val Join_unless = thm "Join_unless";
   109 val Join_constrains_weaken = thm "Join_constrains_weaken";
   110 val JN_constrains_weaken = thm "JN_constrains_weaken";
   111 val JN_stable = thm "JN_stable";
   112 val invariant_JN_I = thm "invariant_JN_I";
   113 val Join_stable = thm "Join_stable";
   114 val Join_increasing = thm "Join_increasing";
   115 val invariant_JoinI = thm "invariant_JoinI";
   116 val FP_JN = thm "FP_JN";
   117 val JN_transient = thm "JN_transient";
   118 val Join_transient = thm "Join_transient";
   119 val Join_transient_I1 = thm "Join_transient_I1";
   120 val Join_transient_I2 = thm "Join_transient_I2";
   121 val JN_ensures = thm "JN_ensures";
   122 val Join_ensures = thm "Join_ensures";
   123 val stable_Join_constrains = thm "stable_Join_constrains";
   124 val stable_Join_Always1 = thm "stable_Join_Always1";
   125 val stable_Join_Always2 = thm "stable_Join_Always2";
   126 val stable_Join_ensures1 = thm "stable_Join_ensures1";
   127 val stable_Join_ensures2 = thm "stable_Join_ensures2";
   128 val ok_SKIP1 = thm "ok_SKIP1";
   129 val ok_SKIP2 = thm "ok_SKIP2";
   130 val ok_Join_commute = thm "ok_Join_commute";
   131 val ok_commute = thm "ok_commute";
   132 val ok_sym = thm "ok_sym";
   133 val ok_iff_OK = thm "ok_iff_OK";
   134 val ok_Join_iff1 = thm "ok_Join_iff1";
   135 val ok_Join_iff2 = thm "ok_Join_iff2";
   136 val ok_Join_commute_I = thm "ok_Join_commute_I";
   137 val ok_JN_iff1 = thm "ok_JN_iff1";
   138 val ok_JN_iff2 = thm "ok_JN_iff2";
   139 val OK_iff_ok = thm "OK_iff_ok";
   140 val OK_imp_ok = thm "OK_imp_ok";
   141 val Allowed_SKIP = thm "Allowed_SKIP";
   142 val Allowed_Join = thm "Allowed_Join";
   143 val Allowed_JN = thm "Allowed_JN";
   144 val ok_iff_Allowed = thm "ok_iff_Allowed";
   145 val OK_iff_Allowed = thm "OK_iff_Allowed";
   146 val safety_prop_Acts_iff = thm "safety_prop_Acts_iff";
   147 val safety_prop_AllowedActs_iff_Allowed = thm "safety_prop_AllowedActs_iff_Allowed";
   148 val Allowed_eq = thm "Allowed_eq";
   149 val def_prg_Allowed = thm "def_prg_Allowed";
   150 val safety_prop_constrains = thm "safety_prop_constrains";
   151 val safety_prop_stable = thm "safety_prop_stable";
   152 val safety_prop_Int = thm "safety_prop_Int";
   153 val safety_prop_INTER1 = thm "safety_prop_INTER1";
   154 val safety_prop_INTER = thm "safety_prop_INTER";
   155 val def_UNION_ok_iff = thm "def_UNION_ok_iff";
   156 
   157 (*Comp*)
   158 val preserves_def = thm "preserves_def";
   159 val funPair_def = thm "funPair_def";
   160 val componentI = thm "componentI";
   161 val component_eq_subset = thm "component_eq_subset";
   162 val component_SKIP = thm "component_SKIP";
   163 val component_refl = thm "component_refl";
   164 val SKIP_minimal = thm "SKIP_minimal";
   165 val component_Join1 = thm "component_Join1";
   166 val component_Join2 = thm "component_Join2";
   167 val Join_absorb1 = thm "Join_absorb1";
   168 val Join_absorb2 = thm "Join_absorb2";
   169 val JN_component_iff = thm "JN_component_iff";
   170 val component_JN = thm "component_JN";
   171 val component_trans = thm "component_trans";
   172 val component_antisym = thm "component_antisym";
   173 val Join_component_iff = thm "Join_component_iff";
   174 val component_constrains = thm "component_constrains";
   175 val program_less_le = thm "program_less_le";
   176 val preservesI = thm "preservesI";
   177 val preserves_imp_eq = thm "preserves_imp_eq";
   178 val Join_preserves = thm "Join_preserves";
   179 val JN_preserves = thm "JN_preserves";
   180 val SKIP_preserves = thm "SKIP_preserves";
   181 val funPair_apply = thm "funPair_apply";
   182 val preserves_funPair = thm "preserves_funPair";
   183 val funPair_o_distrib = thm "funPair_o_distrib";
   184 val fst_o_funPair = thm "fst_o_funPair";
   185 val snd_o_funPair = thm "snd_o_funPair";
   186 val subset_preserves_o = thm "subset_preserves_o";
   187 val preserves_subset_stable = thm "preserves_subset_stable";
   188 val preserves_subset_increasing = thm "preserves_subset_increasing";
   189 val preserves_id_subset_stable = thm "preserves_id_subset_stable";
   190 val safety_prop_preserves = thm "safety_prop_preserves";
   191 val stable_localTo_stable2 = thm "stable_localTo_stable2";
   192 val Increasing_preserves_Stable = thm "Increasing_preserves_Stable";
   193 val component_of_imp_component = thm "component_of_imp_component";
   194 val component_of_refl = thm "component_of_refl";
   195 val component_of_SKIP = thm "component_of_SKIP";
   196 val component_of_trans = thm "component_of_trans";
   197 val strict_component_of_eq = thm "strict_component_of_eq";
   198 val localize_Init_eq = thm "localize_Init_eq";
   199 val localize_Acts_eq = thm "localize_Acts_eq";
   200 val localize_AllowedActs_eq = thm "localize_AllowedActs_eq";
   201 
   202 (*Guar*)
   203 val guar_def = thm "guar_def";
   204 val OK_insert_iff = thm "OK_insert_iff";
   205 val ex1 = thm "ex1";
   206 val ex2 = thm "ex2";
   207 val ex_prop_finite = thm "ex_prop_finite";
   208 val ex_prop_equiv = thm "ex_prop_equiv";
   209 val uv1 = thm "uv1";
   210 val uv2 = thm "uv2";
   211 val uv_prop_finite = thm "uv_prop_finite";
   212 val guaranteesI = thm "guaranteesI";
   213 val guaranteesD = thm "guaranteesD";
   214 val component_guaranteesD = thm "component_guaranteesD";
   215 val guarantees_weaken = thm "guarantees_weaken";
   216 val subset_imp_guarantees_UNIV = thm "subset_imp_guarantees_UNIV";
   217 val subset_imp_guarantees = thm "subset_imp_guarantees";
   218 val ex_prop_imp = thm "ex_prop_imp";
   219 val guarantees_imp = thm "guarantees_imp";
   220 val ex_prop_equiv2 = thm "ex_prop_equiv2";
   221 val guarantees_UN_left = thm "guarantees_UN_left";
   222 val guarantees_Un_left = thm "guarantees_Un_left";
   223 val guarantees_INT_right = thm "guarantees_INT_right";
   224 val guarantees_Int_right = thm "guarantees_Int_right";
   225 val guarantees_Int_right_I = thm "guarantees_Int_right_I";
   226 val guarantees_INT_right_iff = thm "guarantees_INT_right_iff";
   227 val shunting = thm "shunting";
   228 val contrapositive = thm "contrapositive";
   229 val combining1 = thm "combining1";
   230 val combining2 = thm "combining2";
   231 val all_guarantees = thm "all_guarantees";
   232 val ex_guarantees = thm "ex_guarantees";
   233 val guarantees_Join_Int = thm "guarantees_Join_Int";
   234 val guarantees_Join_Un = thm "guarantees_Join_Un";
   235 val guarantees_JN_INT = thm "guarantees_JN_INT";
   236 val guarantees_JN_UN = thm "guarantees_JN_UN";
   237 val guarantees_Join_I1 = thm "guarantees_Join_I1";
   238 val guarantees_Join_I2 = thm "guarantees_Join_I2";
   239 val guarantees_JN_I = thm "guarantees_JN_I";
   240 val Join_welldef_D1 = thm "Join_welldef_D1";
   241 val Join_welldef_D2 = thm "Join_welldef_D2";
   242 val refines_refl = thm "refines_refl";
   243 val ex_refinement_thm = thm "ex_refinement_thm";
   244 val uv_refinement_thm = thm "uv_refinement_thm";
   245 val guarantees_equiv = thm "guarantees_equiv";
   246 val wg_weakest = thm "wg_weakest";
   247 val wg_guarantees = thm "wg_guarantees";
   248 val wg_equiv = thm "wg_equiv";
   249 val component_of_wg = thm "component_of_wg";
   250 val wg_finite = thm "wg_finite";
   251 val wg_ex_prop = thm "wg_ex_prop";
   252 val wx_subset = thm "wx_subset";
   253 val wx_ex_prop = thm "wx_ex_prop";
   254 val wx_weakest = thm "wx_weakest";
   255 val wx'_ex_prop = thm "wx'_ex_prop";
   256 val wx_equiv = thm "wx_equiv";
   257 val guarantees_wx_eq = thm "guarantees_wx_eq";
   258 val stable_guarantees_Always = thm "stable_guarantees_Always";
   259 val leadsTo_Basis = thm "leadsTo_Basis";
   260 val constrains_guarantees_leadsTo = thm "constrains_guarantees_leadsTo";
   261 
   262 (*Extend*)
   263 val Restrict_iff = thm "Restrict_iff";
   264 val Restrict_UNIV = thm "Restrict_UNIV";
   265 val Restrict_empty = thm "Restrict_empty";
   266 val Restrict_Int = thm "Restrict_Int";
   267 val Restrict_triv = thm "Restrict_triv";
   268 val Restrict_subset = thm "Restrict_subset";
   269 val Restrict_eq_mono = thm "Restrict_eq_mono";
   270 val Restrict_imageI = thm "Restrict_imageI";
   271 val Domain_Restrict = thm "Domain_Restrict";
   272 val Image_Restrict = thm "Image_Restrict";
   273 val insert_Id_image_Acts = thm "insert_Id_image_Acts";
   274 val good_mapI = thm "good_mapI";
   275 val good_map_is_surj = thm "good_map_is_surj";
   276 val fst_inv_equalityI = thm "fst_inv_equalityI";
   277 val project_set_iff = thm "project_set_iff";
   278 val extend_set_mono = thm "extend_set_mono";
   279 val extend_set_empty = thm "extend_set_empty";
   280 val project_set_Int_subset = thm "project_set_Int_subset";
   281 val Init_extend = thm "Init_extend";
   282 val Init_project = thm "Init_project";
   283 val Acts_project = thm "Acts_project";
   284 val project_set_UNIV = thm "project_set_UNIV";
   285 val project_set_Union = thm "project_set_Union";
   286 val project_act_mono = thm "project_act_mono";
   287 val project_constrains_project_set = thm "project_constrains_project_set";
   288 val project_stable_project_set = thm "project_stable_project_set";
   289 
   290 
   291 (*Rename*)
   292 val good_map_bij = thm "good_map_bij";
   293 val fst_o_inv_eq_inv = thm "fst_o_inv_eq_inv";
   294 val mem_rename_set_iff = thm "mem_rename_set_iff";
   295 val extend_set_eq_image = thm "extend_set_eq_image";
   296 val Init_rename = thm "Init_rename";
   297 val extend_set_inv = thm "extend_set_inv";
   298 val bij_extend_act_eq_project_act = thm "bij_extend_act_eq_project_act";
   299 val bij_extend_act = thm "bij_extend_act";
   300 val bij_project_act = thm "bij_project_act";
   301 val bij_inv_project_act_eq = thm "bij_inv_project_act_eq";
   302 val Acts_project = thm "Acts_project";
   303 val extend_inv = thm "extend_inv";
   304 val rename_inv_rename = thm "rename_inv_rename";
   305 val rename_rename_inv = thm "rename_rename_inv";
   306 val rename_inv_eq = thm "rename_inv_eq";
   307 val bij_extend = thm "bij_extend";
   308 val bij_project = thm "bij_project";
   309 val inv_project_eq = thm "inv_project_eq";
   310 val Allowed_rename = thm "Allowed_rename";
   311 val bij_rename = thm "bij_rename";
   312 val surj_rename = thm "surj_rename";
   313 val inj_rename_imp_inj = thm "inj_rename_imp_inj";
   314 val surj_rename_imp_surj = thm "surj_rename_imp_surj";
   315 val bij_rename_imp_bij = thm "bij_rename_imp_bij";
   316 val bij_rename_iff = thm "bij_rename_iff";
   317 val rename_SKIP = thm "rename_SKIP";
   318 val rename_Join = thm "rename_Join";
   319 val rename_JN = thm "rename_JN";
   320 val rename_constrains = thm "rename_constrains";
   321 val rename_stable = thm "rename_stable";
   322 val rename_invariant = thm "rename_invariant";
   323 val rename_increasing = thm "rename_increasing";
   324 val reachable_rename_eq = thm "reachable_rename_eq";
   325 val rename_Constrains = thm "rename_Constrains";
   326 val rename_Stable = thm "rename_Stable";
   327 val rename_Always = thm "rename_Always";
   328 val rename_Increasing = thm "rename_Increasing";
   329 val rename_transient = thm "rename_transient";
   330 val rename_ensures = thm "rename_ensures";
   331 val rename_leadsTo = thm "rename_leadsTo";
   332 val rename_LeadsTo = thm "rename_LeadsTo";
   333 val rename_rename_guarantees_eq = thm "rename_rename_guarantees_eq";
   334 val rename_guarantees_eq_rename_inv = thm "rename_guarantees_eq_rename_inv";
   335 val rename_preserves = thm "rename_preserves";
   336 val ok_rename_iff = thm "ok_rename_iff";
   337 val OK_rename_iff = thm "OK_rename_iff";
   338 val bij_eq_rename = thm "bij_eq_rename";
   339 val rename_image_constrains = thm "rename_image_constrains";
   340 val rename_image_stable = thm "rename_image_stable";
   341 val rename_image_increasing = thm "rename_image_increasing";
   342 val rename_image_invariant = thm "rename_image_invariant";
   343 val rename_image_Constrains = thm "rename_image_Constrains";
   344 val rename_image_preserves = thm "rename_image_preserves";
   345 val rename_image_Stable = thm "rename_image_Stable";
   346 val rename_image_Increasing = thm "rename_image_Increasing";
   347 val rename_image_Always = thm "rename_image_Always";
   348 val rename_image_leadsTo = thm "rename_image_leadsTo";
   349 val rename_image_LeadsTo = thm "rename_image_LeadsTo";
   350 
   351 
   352 
   353 (*Lift_prog*)
   354 val sub_def = thm "sub_def";
   355 val lift_map_def = thm "lift_map_def";
   356 val drop_map_def = thm "drop_map_def";
   357 val insert_map_inverse = thm "insert_map_inverse";
   358 val insert_map_delete_map_eq = thm "insert_map_delete_map_eq";
   359 val insert_map_inject1 = thm "insert_map_inject1";
   360 val insert_map_inject2 = thm "insert_map_inject2";
   361 val insert_map_inject = thm "insert_map_inject";
   362 val insert_map_inject = thm "insert_map_inject";
   363 val lift_map_eq_iff = thm "lift_map_eq_iff";
   364 val drop_map_lift_map_eq = thm "drop_map_lift_map_eq";
   365 val inj_lift_map = thm "inj_lift_map";
   366 val lift_map_drop_map_eq = thm "lift_map_drop_map_eq";
   367 val drop_map_inject = thm "drop_map_inject";
   368 val surj_lift_map = thm "surj_lift_map";
   369 val bij_lift_map = thm "bij_lift_map";
   370 val inv_lift_map_eq = thm "inv_lift_map_eq";
   371 val inv_drop_map_eq = thm "inv_drop_map_eq";
   372 val bij_drop_map = thm "bij_drop_map";
   373 val sub_apply = thm "sub_apply";
   374 val lift_set_empty = thm "lift_set_empty";
   375 val lift_set_iff = thm "lift_set_iff";
   376 val lift_set_iff2 = thm "lift_set_iff2";
   377 val lift_set_mono = thm "lift_set_mono";
   378 val lift_set_Un_distrib = thm "lift_set_Un_distrib";
   379 val lift_set_Diff_distrib = thm "lift_set_Diff_distrib";
   380 val bij_lift = thm "bij_lift";
   381 val lift_SKIP = thm "lift_SKIP";
   382 val lift_Join = thm "lift_Join";
   383 val lift_JN = thm "lift_JN";
   384 val lift_constrains = thm "lift_constrains";
   385 val lift_stable = thm "lift_stable";
   386 val lift_invariant = thm "lift_invariant";
   387 val lift_Constrains = thm "lift_Constrains";
   388 val lift_Stable = thm "lift_Stable";
   389 val lift_Always = thm "lift_Always";
   390 val lift_transient = thm "lift_transient";
   391 val lift_ensures = thm "lift_ensures";
   392 val lift_leadsTo = thm "lift_leadsTo";
   393 val lift_LeadsTo = thm "lift_LeadsTo";
   394 val lift_lift_guarantees_eq = thm "lift_lift_guarantees_eq";
   395 val lift_guarantees_eq_lift_inv = thm "lift_guarantees_eq_lift_inv";
   396 val lift_preserves_snd_I = thm "lift_preserves_snd_I";
   397 val delete_map_eqE = thm "delete_map_eqE";
   398 val delete_map_eqE = thm "delete_map_eqE";
   399 val delete_map_neq_apply = thm "delete_map_neq_apply";
   400 val vimage_o_fst_eq = thm "vimage_o_fst_eq";
   401 val vimage_sub_eq_lift_set = thm "vimage_sub_eq_lift_set";
   402 val mem_lift_act_iff = thm "mem_lift_act_iff";
   403 val preserves_snd_lift_stable = thm "preserves_snd_lift_stable";
   404 val constrains_imp_lift_constrains = thm "constrains_imp_lift_constrains";
   405 val insert_map_upd_same = thm "insert_map_upd_same";
   406 val insert_map_upd = thm "insert_map_upd";
   407 val insert_map_eq_diff = thm "insert_map_eq_diff";
   408 val lift_map_eq_diff = thm "lift_map_eq_diff";
   409 val lift_transient_eq_disj = thm "lift_transient_eq_disj";
   410 val lift_map_image_Times = thm "lift_map_image_Times";
   411 val lift_preserves_eq = thm "lift_preserves_eq";
   412 val lift_preserves_sub = thm "lift_preserves_sub";
   413 val o_equiv_assoc = thm "o_equiv_assoc";
   414 val o_equiv_apply = thm "o_equiv_apply";
   415 val fst_o_lift_map = thm "fst_o_lift_map";
   416 val snd_o_lift_map = thm "snd_o_lift_map";
   417 val extend_act_extend_act = thm "extend_act_extend_act";
   418 val project_act_project_act = thm "project_act_project_act";
   419 val project_act_extend_act = thm "project_act_extend_act";
   420 val act_in_UNION_preserves_fst = thm "act_in_UNION_preserves_fst";
   421 val UNION_OK_lift_I = thm "UNION_OK_lift_I";
   422 val OK_lift_I = thm "OK_lift_I";
   423 val Allowed_lift = thm "Allowed_lift";
   424 val lift_image_preserves = thm "lift_image_preserves";
   425 
   426 
   427 (*PPROD*)
   428 val Init_PLam = thm "Init_PLam";
   429 val PLam_empty = thm "PLam_empty";
   430 val PLam_SKIP = thm "PLam_SKIP";
   431 val PLam_insert = thm "PLam_insert";
   432 val PLam_component_iff = thm "PLam_component_iff";
   433 val component_PLam = thm "component_PLam";
   434 val PLam_constrains = thm "PLam_constrains";
   435 val PLam_stable = thm "PLam_stable";
   436 val PLam_transient = thm "PLam_transient";
   437 val PLam_ensures = thm "PLam_ensures";
   438 val PLam_leadsTo_Basis = thm "PLam_leadsTo_Basis";
   439 val invariant_imp_PLam_invariant = thm "invariant_imp_PLam_invariant";
   440 val PLam_preserves_fst = thm "PLam_preserves_fst";
   441 val PLam_preserves_snd = thm "PLam_preserves_snd";
   442 val guarantees_PLam_I = thm "guarantees_PLam_I";
   443 val Allowed_PLam = thm "Allowed_PLam";
   444 val PLam_preserves = thm "PLam_preserves";
   445 
   446 (*Follows*)
   447 val mono_Always_o = thm "mono_Always_o";
   448 val mono_LeadsTo_o = thm "mono_LeadsTo_o";
   449 val Follows_constant = thm "Follows_constant";
   450 val mono_Follows_o = thm "mono_Follows_o";
   451 val mono_Follows_apply = thm "mono_Follows_apply";
   452 val Follows_trans = thm "Follows_trans";
   453 val Follows_Increasing1 = thm "Follows_Increasing1";
   454 val Follows_Increasing2 = thm "Follows_Increasing2";
   455 val Follows_Bounded = thm "Follows_Bounded";
   456 val Follows_LeadsTo = thm "Follows_LeadsTo";
   457 val Follows_LeadsTo_pfixLe = thm "Follows_LeadsTo_pfixLe";
   458 val Follows_LeadsTo_pfixGe = thm "Follows_LeadsTo_pfixGe";
   459 val Always_Follows1 = thm "Always_Follows1";
   460 val Always_Follows2 = thm "Always_Follows2";
   461 val increasing_Un = thm "increasing_Un";
   462 val Increasing_Un = thm "Increasing_Un";
   463 val Always_Un = thm "Always_Un";
   464 val Follows_Un_lemma = thm "Follows_Un_lemma";
   465 val Follows_Un = thm "Follows_Un";
   466 val increasing_union = thm "increasing_union";
   467 val Increasing_union = thm "Increasing_union";
   468 val Always_union = thm "Always_union";
   469 val Follows_union_lemma = thm "Follows_union_lemma";
   470 val Follows_union = thm "Follows_union";
   471 val Follows_setsum = thm "Follows_setsum";
   472 val Increasing_imp_Stable_pfixGe = thm "Increasing_imp_Stable_pfixGe";
   473 val LeadsTo_le_imp_pfixGe = thm "LeadsTo_le_imp_pfixGe";
   474 
   475 
   476 (*proves "co" properties when the program is specified*)
   477 fun gen_constrains_tac(cs,ss) i = 
   478    SELECT_GOAL
   479       (EVERY [REPEAT (Always_Int_tac 1),
   480 	      REPEAT (etac Always_ConstrainsI 1
   481 		      ORELSE
   482 		      resolve_tac [StableI, stableI,
   483 				   constrains_imp_Constrains] 1),
   484 	      rtac constrainsI 1,
   485 	      full_simp_tac ss 1,
   486 	      REPEAT (FIRSTGOAL (etac disjE)),
   487 	      ALLGOALS (clarify_tac cs),
   488 	      ALLGOALS (asm_lr_simp_tac ss)]) i;
   489 
   490 (*proves "ensures/leadsTo" properties when the program is specified*)
   491 fun gen_ensures_tac(cs,ss) sact = 
   492     SELECT_GOAL
   493       (EVERY [REPEAT (Always_Int_tac 1),
   494 	      etac Always_LeadsTo_Basis 1 
   495 	          ORELSE   (*subgoal may involve LeadsTo, leadsTo or ensures*)
   496 		  REPEAT (ares_tac [LeadsTo_Basis, leadsTo_Basis,
   497 				    EnsuresI, ensuresI] 1),
   498 	      (*now there are two subgoals: co & transient*)
   499 	      simp_tac ss 2,
   500 	      res_inst_tac [("act", sact)] transientI 2,
   501                  (*simplify the command's domain*)
   502 	      simp_tac (ss addsimps [Domain_def]) 3,
   503 	      gen_constrains_tac (cs,ss) 1,
   504 	      ALLGOALS (clarify_tac cs),
   505 	      ALLGOALS (asm_lr_simp_tac ss)]);
   506 
   507 fun ensures_tac sact = gen_ensures_tac (claset(), simpset()) sact;
   508 
   509 
   510 (*Composition equivalences, from Lift_prog*)
   511 
   512 fun make_o_equivs th =
   513     [th,
   514      th RS o_equiv_assoc |> simplify (HOL_ss addsimps [o_assoc]),
   515      th RS o_equiv_apply |> simplify (HOL_ss addsimps [o_def, sub_def])];
   516 
   517 Addsimps (make_o_equivs fst_o_funPair @ make_o_equivs snd_o_funPair);
   518 
   519 Addsimps (make_o_equivs fst_o_lift_map @ make_o_equivs snd_o_lift_map);