|
13786
|
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 |
|
|
13796
|
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 |
|
|
13792
|
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 |
|
|
13790
|
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 |
|
|
13786
|
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 |
|
|
13796
|
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 |
|
|
13786
|
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 |
|
|
13796
|
507 |
fun ensures_tac sact = gen_ensures_tac (claset(), simpset()) sact;
|
|
|
508 |
|
|
13786
|
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);
|