author | paulson |
Fri, 07 May 1999 10:50:28 +0200 | |
changeset 6614 | 2d47dee036b5 |
parent 6570 | a7d7985050a9 |
child 6676 | 62d1e642da30 |
permissions | -rw-r--r-- |
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(* Title: HOL/UNITY/Lift |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1998 University of Cambridge |
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|
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The Lift-Control Example |
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*) |
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(*split_all_tac causes a big blow-up*) |
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claset_ref() := claset() delSWrapper record_split_name; |
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5563 | 12 |
Goal "[| x ~: A; y : A |] ==> x ~= y"; |
13 |
by (Blast_tac 1); |
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14 |
qed "not_mem_distinct"; |
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15 |
||
16 |
fun distinct_tac i = |
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17 |
dtac zle_neq_implies_zless i THEN |
|
18 |
eresolve_tac [not_mem_distinct, not_mem_distinct RS not_sym] i THEN |
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19 |
assume_tac i; |
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||
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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(** Rules to move "metric n s" out of the assumptions, for case splitting **) |
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val mov_metric1 = read_instantiate_sg (sign_of thy) |
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[("P", "?x < metric ?n ?s")] rev_mp; |
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26 |
val mov_metric2 = read_instantiate_sg (sign_of thy) |
5596 | 27 |
[("P", "?x = metric ?n ?s")] rev_mp; |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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val mov_metric3 = read_instantiate_sg (sign_of thy) |
5596 | 30 |
[("P", "~ (?x < metric ?n ?s)")] rev_mp; |
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val mov_metric4 = read_instantiate_sg (sign_of thy) |
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[("P", "(?x <= metric ?n ?s)")] rev_mp; |
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(*The order in which they are applied seems to be critical...*) |
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val mov_metrics = [mov_metric2, mov_metric3, mov_metric1, mov_metric4]; |
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val metric_simps = [metric_def, vimage_def]; |
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Addsimps [Lprg_def RS def_prg_Init]; |
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program_defs_ref := [Lprg_def]; |
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Addsimps (map simp_of_act |
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[request_act_def, open_act_def, close_act_def, |
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req_up_def, req_down_def, move_up_def, move_down_def, |
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button_press_def]); |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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val always_defs = [above_def, below_def, queueing_def, |
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goingup_def, goingdown_def, ready_def]; |
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Addsimps (map simp_of_set always_defs); |
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val LeadsTo_Trans_Un' = rotate_prems 1 LeadsTo_Trans_Un; |
6614 | 56 |
(* [| Lprg: B LeadsTo C; Lprg: A LeadsTo B |] ==> Lprg: (A Un B) LeadsTo C *) |
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(*Simplification for records*) |
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Addsimps (thms"state.update_defs"); |
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Addsimps [bounded_def, open_stop_def, open_move_def, stop_floor_def, |
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moving_up_def, moving_down_def]; |
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5357 | 65 |
AddIffs [Min_le_Max]; |
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5320 | 67 |
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Goal "Lprg : Always open_stop"; |
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by (rtac AlwaysI 1); |
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by (Force_tac 1); |
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by (constrains_tac 1); |
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qed "open_stop"; |
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73 |
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Goal "Lprg : Always stop_floor"; |
75 |
by (rtac AlwaysI 1); |
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by (Force_tac 1); |
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by (constrains_tac 1); |
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qed "stop_floor"; |
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Constrains, Stable, Invariant...more of the substitution axiom, but Union
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(*This one needs open_stop, which was proved above*) |
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Goal "Lprg : Always open_move"; |
82 |
by (rtac AlwaysI 1); |
|
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by (rtac (open_stop RS Always_ConstrainsI RS StableI) 2); |
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by (Force_tac 1); |
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by (constrains_tac 1); |
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qed "open_move"; |
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Goal "Lprg : Always moving_up"; |
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by (rtac AlwaysI 1); |
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by (Force_tac 1); |
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by (constrains_tac 1); |
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by (blast_tac (claset() addDs [zle_imp_zless_or_eq]) 1); |
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qed "moving_up"; |
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6570 | 95 |
Goal "Lprg : Always moving_down"; |
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by (rtac AlwaysI 1); |
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by (Force_tac 1); |
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by (constrains_tac 1); |
5563 | 99 |
by (blast_tac (claset() addDs [zle_imp_zless_or_eq]) 1); |
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qed "moving_down"; |
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101 |
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6570 | 102 |
Goal "Lprg : Always bounded"; |
103 |
by (rtac AlwaysI 1); |
|
104 |
by (rtac (Always_Int_rule [moving_up, moving_down] RS Always_StableI) 2); |
|
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by (Force_tac 1); |
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by (constrains_tac 1); |
5563 | 107 |
by (ALLGOALS Clarify_tac); |
108 |
by (REPEAT_FIRST distinct_tac); |
|
6161 | 109 |
by Auto_tac; |
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qed "bounded"; |
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(*** Progress ***) |
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val abbrev_defs = [moving_def, stopped_def, |
5340 | 118 |
opened_def, closed_def, atFloor_def, Req_def]; |
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Addsimps (map simp_of_set abbrev_defs); |
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(** The HUG'93 paper mistakenly omits the Req n from these! **) |
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(** Lift_1 **) |
126 |
||
6536 | 127 |
Goal "Lprg : (stopped Int atFloor n) LeadsTo (opened Int atFloor n)"; |
5340 | 128 |
by (cut_facts_tac [stop_floor] 1); |
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129 |
by (ensures_tac "open_act" 1); |
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130 |
qed "E_thm01"; (*lem_lift_1_5*) |
5340 | 131 |
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6536 | 132 |
Goal "Lprg : (Req n Int stopped - atFloor n) LeadsTo \ |
6139 | 133 |
\ (Req n Int opened - atFloor n)"; |
5340 | 134 |
by (cut_facts_tac [stop_floor] 1); |
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135 |
by (ensures_tac "open_act" 1); |
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136 |
qed "E_thm02"; (*lem_lift_1_1*) |
5340 | 137 |
|
6536 | 138 |
Goal "Lprg : (Req n Int opened - atFloor n) LeadsTo \ |
6139 | 139 |
\ (Req n Int closed - (atFloor n - queueing))"; |
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140 |
by (ensures_tac "close_act" 1); |
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141 |
qed "E_thm03"; (*lem_lift_1_2*) |
5340 | 142 |
|
6536 | 143 |
Goal "Lprg : (Req n Int closed Int (atFloor n - queueing)) \ |
144 |
\ LeadsTo (opened Int atFloor n)"; |
|
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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145 |
by (ensures_tac "open_act" 1); |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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146 |
qed "E_thm04"; (*lem_lift_1_7*) |
5340 | 147 |
|
148 |
||
5357 | 149 |
(** Lift 2. Statements of thm05a and thm05b were wrong! **) |
5340 | 150 |
|
151 |
Open_locale "floor"; |
|
152 |
||
5357 | 153 |
val Min_le_n = thm "Min_le_n"; |
154 |
val n_le_Max = thm "n_le_Max"; |
|
155 |
||
156 |
AddIffs [Min_le_n, n_le_Max]; |
|
5340 | 157 |
|
5563 | 158 |
val le_MinD = Min_le_n RS zle_anti_sym; |
159 |
val Max_leD = n_le_Max RSN (2,zle_anti_sym); |
|
5357 | 160 |
|
5563 | 161 |
AddSDs [le_MinD, zleI RS le_MinD, |
162 |
Max_leD, zleI RS Max_leD]; |
|
5357 | 163 |
|
164 |
(*lem_lift_2_0 |
|
165 |
NOT an ensures property, but a mere inclusion; |
|
166 |
don't know why script lift_2.uni says ENSURES*) |
|
6536 | 167 |
Goal "Lprg : (Req n Int closed - (atFloor n - queueing)) \ |
168 |
\ LeadsTo ((closed Int goingup Int Req n) Un \ |
|
6139 | 169 |
\ (closed Int goingdown Int Req n))"; |
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170 |
by (rtac subset_imp_LeadsTo 1); |
5563 | 171 |
by (auto_tac (claset() addSEs [int_neqE], simpset())); |
5340 | 172 |
qed "E_thm05c"; |
173 |
||
5357 | 174 |
(*lift_2*) |
6536 | 175 |
Goal "Lprg : (Req n Int closed - (atFloor n - queueing)) \ |
176 |
\ LeadsTo (moving Int Req n)"; |
|
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177 |
by (rtac ([E_thm05c, LeadsTo_Un] MRS LeadsTo_Trans) 1); |
566f47250bd0
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178 |
by (ensures_tac "req_down" 2); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
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179 |
by (ensures_tac "req_up" 1); |
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180 |
by Auto_tac; |
5340 | 181 |
qed "lift_2"; |
182 |
||
183 |
||
5357 | 184 |
(** Towards lift_4 ***) |
5563 | 185 |
|
5357 | 186 |
|
187 |
(*lem_lift_4_1 *) |
|
5563 | 188 |
Goal "#0 < N ==> \ |
6536 | 189 |
\ Lprg : (moving Int Req n Int {s. metric n s = N} Int \ |
190 |
\ {s. floor s ~: req s} Int {s. up s}) \ |
|
191 |
\ LeadsTo \ |
|
6139 | 192 |
\ (moving Int Req n Int {s. metric n s < N})"; |
5357 | 193 |
by (cut_facts_tac [moving_up] 1); |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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|
194 |
by (ensures_tac "move_up" 1); |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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|
195 |
by Safe_tac; |
5357 | 196 |
(*this step consolidates two formulae to the goal metric n s' <= metric n s*) |
5563 | 197 |
by (etac (zleI RS zle_anti_sym RS sym) 1); |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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|
198 |
by (REPEAT_FIRST (eresolve_tac mov_metrics)); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
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|
199 |
by (REPEAT_FIRST distinct_tac); |
5563 | 200 |
(** LEVEL 6 **) |
5583 | 201 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps |
202 |
[zle_def] @ metric_simps @ zcompare_rls))); |
|
5357 | 203 |
qed "E_thm12a"; |
204 |
||
205 |
||
206 |
||
207 |
(*lem_lift_4_3 *) |
|
5563 | 208 |
Goal "#0 < N ==> \ |
6536 | 209 |
\ Lprg : (moving Int Req n Int {s. metric n s = N} Int \ |
210 |
\ {s. floor s ~: req s} - {s. up s}) \ |
|
211 |
\ LeadsTo (moving Int Req n Int {s. metric n s < N})"; |
|
5357 | 212 |
by (cut_facts_tac [moving_down] 1); |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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|
213 |
by (ensures_tac "move_down" 1); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
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|
214 |
by Safe_tac; |
5357 | 215 |
(*this step consolidates two formulae to the goal metric n s' <= metric n s*) |
5563 | 216 |
by (etac (zleI RS zle_anti_sym RS sym) 1); |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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parents:
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|
217 |
by (REPEAT_FIRST (eresolve_tac mov_metrics)); |
5563 | 218 |
by (REPEAT_FIRST distinct_tac); |
219 |
(** LEVEL 6 **) |
|
6139 | 220 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps metric_simps @ zcompare_rls))); |
5357 | 221 |
qed "E_thm12b"; |
222 |
||
223 |
(*lift_4*) |
|
6536 | 224 |
Goal "#0<N ==> Lprg : (moving Int Req n Int {s. metric n s = N} Int \ |
225 |
\ {s. floor s ~: req s}) LeadsTo \ |
|
5563 | 226 |
\ (moving Int Req n Int {s. metric n s < N})"; |
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A new approach, using simp_of_act and simp_of_set to activate definitions when
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|
227 |
by (rtac ([subset_imp_LeadsTo, LeadsTo_Un] MRS LeadsTo_Trans) 1); |
5583 | 228 |
by (etac E_thm12b 3); |
229 |
by (etac E_thm12a 2); |
|
5357 | 230 |
by (Blast_tac 1); |
231 |
qed "lift_4"; |
|
232 |
||
233 |
||
234 |
(** towards lift_5 **) |
|
235 |
||
236 |
(*lem_lift_5_3*) |
|
5563 | 237 |
Goal "#0<N \ |
6536 | 238 |
\ ==> Lprg : (closed Int Req n Int {s. metric n s = N} Int goingup) LeadsTo \ |
5563 | 239 |
\ (moving Int Req n Int {s. metric n s < N})"; |
5357 | 240 |
by (cut_facts_tac [bounded] 1); |
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
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changeset
|
241 |
by (ensures_tac "req_up" 1); |
5424
771a68a468cc
modified proofs for new constrains_tac and ensures_tac
paulson
parents:
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|
242 |
by Auto_tac; |
5426
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A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
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changeset
|
243 |
by (REPEAT_FIRST (eresolve_tac mov_metrics)); |
6139 | 244 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps metric_simps @ zcompare_rls))); |
6128 | 245 |
by (Blast_tac 1); |
5357 | 246 |
qed "E_thm16a"; |
247 |
||
248 |
(*lem_lift_5_1 has ~goingup instead of goingdown*) |
|
5563 | 249 |
Goal "#0<N ==> \ |
6536 | 250 |
\ Lprg : (closed Int Req n Int {s. metric n s = N} Int goingdown) LeadsTo \ |
5563 | 251 |
\ (moving Int Req n Int {s. metric n s < N})"; |
5357 | 252 |
by (cut_facts_tac [bounded] 1); |
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566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
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changeset
|
253 |
by (ensures_tac "req_down" 1); |
5424
771a68a468cc
modified proofs for new constrains_tac and ensures_tac
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parents:
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|
254 |
by Auto_tac; |
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566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
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changeset
|
255 |
by (REPEAT_FIRST (eresolve_tac mov_metrics)); |
6139 | 256 |
by (ALLGOALS (asm_simp_tac (simpset() addsimps metric_simps @ zcompare_rls))); |
6128 | 257 |
by (Blast_tac 1); |
5357 | 258 |
qed "E_thm16b"; |
259 |
||
260 |
||
261 |
||
262 |
(*lem_lift_5_0 proves an intersection involving ~goingup and goingup, |
|
263 |
i.e. the trivial disjunction, leading to an asymmetrical proof.*) |
|
5563 | 264 |
Goal "#0<N ==> Req n Int {s. metric n s = N} <= goingup Un goingdown"; |
265 |
by (asm_simp_tac (simpset() addsimps metric_simps) 1); |
|
5758
27a2b36efd95
corrected auto_tac (applications of unsafe wrappers)
oheimb
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5706
diff
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|
266 |
by (force_tac (claset() delrules [impCE] addEs [impCE], |
6139 | 267 |
simpset() addsimps conj_comms) 1); |
5357 | 268 |
qed "E_thm16c"; |
269 |
||
270 |
||
271 |
(*lift_5*) |
|
6536 | 272 |
Goal "#0<N ==> Lprg : (closed Int Req n Int {s. metric n s = N}) LeadsTo \ |
5563 | 273 |
\ (moving Int Req n Int {s. metric n s < N})"; |
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
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diff
changeset
|
274 |
by (rtac ([subset_imp_LeadsTo, LeadsTo_Un] MRS LeadsTo_Trans) 1); |
5583 | 275 |
by (etac E_thm16b 3); |
276 |
by (etac E_thm16a 2); |
|
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
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changeset
|
277 |
by (dtac E_thm16c 1); |
5357 | 278 |
by (Blast_tac 1); |
279 |
qed "lift_5"; |
|
280 |
||
281 |
||
282 |
(** towards lift_3 **) |
|
283 |
||
284 |
(*lemma used to prove lem_lift_3_1*) |
|
5563 | 285 |
Goal "[| metric n s = #0; Min <= floor s; floor s <= Max |] ==> floor s = n"; |
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
286 |
by (etac rev_mp 1); |
5563 | 287 |
(*force simplification of "metric..." while in conclusion part*) |
288 |
by (asm_simp_tac (simpset() addsimps metric_simps) 1); |
|
5357 | 289 |
qed "metric_eq_0D"; |
290 |
||
291 |
AddDs [metric_eq_0D]; |
|
292 |
||
293 |
||
294 |
(*lem_lift_3_1*) |
|
6536 | 295 |
Goal "Lprg : (moving Int Req n Int {s. metric n s = #0}) LeadsTo \ |
5357 | 296 |
\ (stopped Int atFloor n)"; |
297 |
by (cut_facts_tac [bounded] 1); |
|
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
298 |
by (ensures_tac "request_act" 1); |
5424
771a68a468cc
modified proofs for new constrains_tac and ensures_tac
paulson
parents:
5410
diff
changeset
|
299 |
by Auto_tac; |
5357 | 300 |
qed "E_thm11"; |
301 |
||
302 |
(*lem_lift_3_5*) |
|
6536 | 303 |
Goal |
304 |
"Lprg : (moving Int Req n Int {s. metric n s = N} Int {s. floor s : req s}) \ |
|
305 |
\ LeadsTo (stopped Int Req n Int {s. metric n s = N} Int {s. floor s : req s})"; |
|
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
306 |
by (ensures_tac "request_act" 1); |
5424
771a68a468cc
modified proofs for new constrains_tac and ensures_tac
paulson
parents:
5410
diff
changeset
|
307 |
by (auto_tac (claset(), simpset() addsimps metric_simps)); |
5357 | 308 |
qed "E_thm13"; |
309 |
||
310 |
(*lem_lift_3_6*) |
|
5563 | 311 |
Goal "#0 < N ==> \ |
6536 | 312 |
\ Lprg : \ |
5563 | 313 |
\ (stopped Int Req n Int {s. metric n s = N} Int {s. floor s : req s}) \ |
6536 | 314 |
\ LeadsTo (opened Int Req n Int {s. metric n s = N})"; |
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
315 |
by (ensures_tac "open_act" 1); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
316 |
by (REPEAT_FIRST (eresolve_tac mov_metrics)); |
5424
771a68a468cc
modified proofs for new constrains_tac and ensures_tac
paulson
parents:
5410
diff
changeset
|
317 |
by (auto_tac (claset(), simpset() addsimps metric_simps)); |
5357 | 318 |
qed "E_thm14"; |
319 |
||
320 |
(*lem_lift_3_7*) |
|
6536 | 321 |
Goal "Lprg : (opened Int Req n Int {s. metric n s = N}) \ |
322 |
\ LeadsTo (closed Int Req n Int {s. metric n s = N})"; |
|
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
323 |
by (ensures_tac "close_act" 1); |
5424
771a68a468cc
modified proofs for new constrains_tac and ensures_tac
paulson
parents:
5410
diff
changeset
|
324 |
by (auto_tac (claset(), simpset() addsimps metric_simps)); |
5357 | 325 |
qed "E_thm15"; |
326 |
||
327 |
||
328 |
(** the final steps **) |
|
329 |
||
5563 | 330 |
Goal "#0 < N ==> \ |
6536 | 331 |
\ Lprg : \ |
5563 | 332 |
\ (moving Int Req n Int {s. metric n s = N} Int {s. floor s : req s}) \ |
6536 | 333 |
\ LeadsTo (moving Int Req n Int {s. metric n s < N})"; |
5479 | 334 |
by (blast_tac (claset() addSIs [E_thm13, E_thm14, E_thm15, lift_5] |
335 |
addIs [LeadsTo_Trans]) 1); |
|
5357 | 336 |
qed "lift_3_Req"; |
337 |
||
338 |
||
5563 | 339 |
|
340 |
(*Now we observe that our integer metric is really a natural number*) |
|
6570 | 341 |
Goal "Lprg : Always {s. #0 <= metric n s}"; |
342 |
by (rtac (bounded RS Always_weaken) 1); |
|
5563 | 343 |
by (simp_tac (simpset() addsimps metric_simps @ zcompare_rls) 1); |
344 |
by (auto_tac (claset(), |
|
345 |
simpset() addsimps [zless_iff_Suc_zadd, zle_iff_zadd])); |
|
346 |
by (REPEAT_FIRST (etac ssubst)); |
|
5583 | 347 |
by (auto_tac (claset(), simpset() addsimps [zadd_int])); |
6570 | 348 |
qed "Always_nonneg"; |
5563 | 349 |
|
6570 | 350 |
val R_thm11 = [Always_nonneg, E_thm11] MRS Always_LeadsTo_weaken; |
5563 | 351 |
|
6536 | 352 |
Goal "Lprg : (moving Int Req n) LeadsTo (stopped Int atFloor n)"; |
6570 | 353 |
by (rtac (Always_nonneg RS integ_0_le_induct) 1); |
5563 | 354 |
by (case_tac "#0 < z" 1); |
355 |
(*If z <= #0 then actually z = #0*) |
|
356 |
by (fold_tac [zle_def]); |
|
357 |
by (force_tac (claset() addIs [R_thm11, zle_anti_sym], simpset()) 2); |
|
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
358 |
by (rtac ([asm_rl, Un_upper1] MRS LeadsTo_weaken_R) 1); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
359 |
by (rtac ([subset_imp_LeadsTo, LeadsTo_Un] MRS LeadsTo_Trans) 1); |
5583 | 360 |
by (rtac lift_3_Req 3); |
361 |
by (rtac lift_4 2); |
|
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
362 |
by Auto_tac; |
5357 | 363 |
qed "lift_3"; |
364 |
||
365 |
||
6536 | 366 |
Goal "Lprg : (Req n) LeadsTo (opened Int atFloor n)"; |
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
367 |
by (rtac LeadsTo_Trans 1); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
368 |
by (rtac (E_thm04 RS LeadsTo_Un) 2); |
5583 | 369 |
by (rtac LeadsTo_Un_post 2); |
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
370 |
by (rtac (E_thm01 RS LeadsTo_Trans_Un') 2); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
371 |
by (rtac (lift_3 RS LeadsTo_Trans_Un') 2); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
372 |
by (rtac (lift_2 RS LeadsTo_Trans_Un') 2); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
373 |
by (rtac (E_thm03 RS LeadsTo_Trans_Un') 2); |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
374 |
by (rtac E_thm02 2); |
6570 | 375 |
by (rtac (open_move RS Always_LeadsToI) 1); |
376 |
by (rtac (open_stop RS Always_LeadsToI) 1); |
|
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
377 |
by (rtac subset_imp_LeadsTo 1); |
5340 | 378 |
by (Clarify_tac 1); |
5484 | 379 |
(*The case split is not essential but makes Blast_tac much faster. |
380 |
Must also be careful to prevent simplification from looping*) |
|
381 |
by (case_tac "open x" 1); |
|
382 |
by (ALLGOALS (rotate_tac ~1)); |
|
383 |
by (ALLGOALS Asm_full_simp_tac); |
|
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5424
diff
changeset
|
384 |
by (Blast_tac 1); |
5340 | 385 |
qed "lift_1"; |
386 |
||
6024 | 387 |
Close_locale "floor"; |