-
Notifications
You must be signed in to change notification settings - Fork 1
/
SecureProofRMM1.v
838 lines (830 loc) · 42.8 KB
/
SecureProofRMM1.v
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
Require Import SpecDeps.
Require Import RData.
Require Import EventReplay.
Require Import MoverTypes.
Require Import Constants.
Require Import CommonLib.
Require Import AbsAccessor.Spec.
Require Import RmiSMC.Spec.
Require Import RefTactics.
Require Import Security.RefRel.
Local Open Scope string_scope.
Local Open Scope Z_scope.
Local Opaque Z.add Z.mul Z.div Z.shiftl Z.shiftr Z.land Z.lor.
Lemma smc_granule_delegate_security:
forall habd habd' labd addr ret
(Hspec: smc_granule_delegate_spec addr habd = Some (habd', ret))
(Hrel: relate_adt habd labd) (rmm_run: cur_rec (priv habd) = None),
exists labd', smc_granule_delegate_spec addr labd = Some (labd', ret) /\ relate_adt habd' labd'.
Proof.
intros. destruct Hrel.
unfold smc_granule_delegate_spec in *.
repeat autounfold in *.
repeat (rewrite_sec_rel; simpl_hyp Hspec; simpl in * ); extract_prop_dec; inv Hspec.
- match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel0). rewrite Hld.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C5. simpl_query_oracle' Hld.
rewrite_sec_rel. simpl_htarget. grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. destruct_zmap; constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data s s0 id_share). reflexivity. assumption.
intros. rewrite (relate_share_g_regs s s0 id_share). reflexivity. assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try reflexivity.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; try assumption; autounfold in *.
* intro gidx. destruct_zmap; simpl. intros; contra. auto.
* intro gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros. apply rec_rd in H. srewrite. omega. auto.
* intros rd_gidx. destruct_zmap; simpl. intros; omega.
intros until b. destruct_zmap; simpl. intros.
exploit (table_prop rd_gidx H ipa_gidx data_gidx); srewrite; try eassumption.
reflexivity. intros (? & ? & ?). omega. apply table_prop; assumption.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega. apply tlb_prop; assumption.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega. apply running_not_new; assumption.
* intros rec_gidx. destruct_zmap; simpl. intros; omega. auto.
+ constructor; simpl; try assumption; autounfold in *.
* intro rd_gidx. destruct_zmap; simpl. intros; omega.
intros. exploit (mem_rel rd_gidx); try eassumption.
destruct_zmap; simpl.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega. auto.
* intros rd_gidx rec_gidx. autounfold. destruct_zmap; simpl. intros. omega.
destruct_zmap. simpl. intros. omega. eapply reg_not_run_rel.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega. intros.
apply cur_running in running. srewrite. contra. assumption.
* intros. rewrite regs_eq_not_realm. reflexivity. assumption.
- match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel). rewrite Hld.
destruct Hrel as (id_share & invs & rel_secure).
simpl_query_oracle' C5. simpl_query_oracle' Hld.
rewrite_sec_rel. simpl_htarget. grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_share. assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_priv. assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try assumption.
+ constructor; simpl; assumption.
- eexists; split. reflexivity.
constructor; simpl; assumption.
Qed.
Lemma smc_granule_undelegate_security:
forall habd habd' labd addr ret
(Hspec: smc_granule_undelegate_spec addr habd = Some (habd', ret))
(Hrel: relate_adt habd labd),
exists labd', smc_granule_undelegate_spec addr labd = Some (labd', ret) /\ relate_adt habd' labd'.
Proof.
intros. destruct Hrel.
unfold smc_granule_undelegate_spec in *.
repeat autounfold in *.
repeat (rewrite_sec_rel; simpl_hyp Hspec; simpl in * ); extract_prop_dec; inv Hspec.
- match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel0). rewrite Hld.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C4. simpl_query_oracle' Hld.
rewrite_sec_rel. simpl_htarget. grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. destruct_zmap; constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data s s0 id_share). reflexivity.
grewrite. autounfold. omega.
intros. rewrite (relate_share_g_regs s s0 id_share). reflexivity.
grewrite. autounfold. omega.
intros. rewrite (relate_share_g_data s s0 id_share). reflexivity. assumption.
intros. rewrite (relate_share_g_regs s s0 id_share). reflexivity. assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try reflexivity.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; try assumption; autounfold in *.
* intro gidx. destruct_zmap; simpl. reflexivity. auto.
* intro gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros. apply rec_rd in H. srewrite. omega. auto.
* intros rd_gidx. destruct_zmap; simpl. intros; omega.
intros until b. destruct_zmap; simpl. intros.
exploit (table_prop rd_gidx H ipa_gidx data_gidx); srewrite; try eassumption.
reflexivity. intros (? & ? & ?). omega. apply table_prop; assumption.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega. apply tlb_prop; assumption.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega. apply running_not_new; assumption.
* intros rec_gidx. destruct_zmap; simpl. intros; omega. auto.
+ constructor; simpl; try assumption; autounfold in *.
* intro rd_gidx. destruct_zmap; simpl. intros; omega.
intros. exploit (mem_rel rd_gidx); try eassumption.
destruct_zmap; simpl.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega. auto.
* intros rd_gidx rec_gidx. autounfold. destruct_zmap; simpl. intros. omega.
destruct_zmap. simpl. intros. omega. eapply reg_not_run_rel.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega. intros.
apply cur_running in running. srewrite. contra. assumption.
* intros. rewrite regs_eq_not_realm. reflexivity. assumption.
- match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel). rewrite Hld.
destruct Hrel as (id_share & invs & rel_secure).
simpl_query_oracle' C4. simpl_query_oracle' Hld.
rewrite_sec_rel. simpl_htarget. grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_share. assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_priv. assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try assumption.
+ constructor; simpl; assumption.
- eexists; split. reflexivity.
constructor; simpl; assumption.
Qed.
Lemma smc_realm_create_security:
forall habd habd' labd rd_addr realm_param_addr ret
(Hspec: smc_realm_create_spec rd_addr realm_param_addr habd = Some (habd', ret))
(Hrel: relate_adt habd labd) (rmm_run: cur_rec (priv habd) = None),
exists labd', smc_realm_create_spec rd_addr realm_param_addr labd = Some (labd', ret) /\ relate_adt habd' labd'.
Proof.
intros. destruct Hrel.
unfold smc_realm_create_spec in *.
repeat autounfold in *.
repeat (rewrite_sec_rel; simpl_hyp Hspec; simpl in * ); extract_prop_dec; inv Hspec.
- repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
assert(Hnd: gtype (gs (share habd)) @ (__addr_to_gidx z0) <> GRANULE_STATE_DATA). autounfold; omega.
repeat rewrite (relate_share_g_data _ _ id_share _ Hnd). grewrite.
simpl in *. red in Prop5. red in Prop6. red in Prop4.
repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
{ duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl; try assumption. }
{ duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl; try assumption. }
intros (ld & Hld & Hrel0). rewrite Hld.
clear id_share rel_secure invs.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C22. simpl_query_oracle' Hld.
repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data _ _ id_share). reflexivity.
grewrite. autounfold; omega.
intros. rewrite (relate_share_g_regs _ _ id_share). reflexivity.
grewrite. autounfold; omega.
destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data _ _ id_share). reflexivity.
grewrite. autounfold; omega.
intros. rewrite (relate_share_g_regs _ _ id_share). reflexivity.
grewrite. autounfold; omega.
destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data _ _ id_share). reflexivity.
grewrite. autounfold; omega.
intros. rewrite (relate_share_g_regs _ _ id_share). reflexivity.
grewrite. autounfold; omega.
destruct id_share; auto.
+ simpl; constructor; simpl; rewrite_sec_rel; try reflexivity.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; try assumption; autounfold in *.
* intro gidx.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
auto.
* intro rd_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros. srewrite.
pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
destruct_zmap; simpl. intros. srewrite.
pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
destruct_zmap; simpl. intros. srewrite.
pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
auto.
* intro rd_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros until b.
intros. rewrite new_table in H0. inv H0.
bool_rel_all; omega. grewrite. omega.
intros until b.
destruct_zmap; simpl. intros. rewrite <- Heq2 in *.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega.
destruct_zmap; simpl. intros. rewrite <- Heq3 in *.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega.
destruct_zmap; simpl. intros. rewrite <- Heq4 in *.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega.
intros. eapply table_prop; eassumption.
* intros rd_gidx rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. apply cur_running in running. srewrite. contra. assumption.
intros. eapply tlb_prop; eassumption.
* intros rd_gidx rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. apply cur_running in running. srewrite. contra. assumption.
apply running_not_new; eassumption.
* intro rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
apply cur_running.
+ constructor; simpl; try assumption; autounfold in *.
* intro rd_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. erewrite new_table in Hwalk. inv Hwalk. srewrite. omega.
intros. destruct_zmap; simpl. rewrite <- Heq2. apply mem_rel; assumption.
destruct_zmap; simpl. rewrite <- Heq3. apply mem_rel; assumption.
destruct_zmap; simpl. rewrite <- Heq4. apply mem_rel; assumption.
apply mem_rel; assumption.
* intros rd_gidx rec_gidx. autounfold.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. pose proof (rec_rd rec_gidx). apply H in is_rec. srewrite. omega.
apply reg_not_run_rel.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. apply cur_running in running. srewrite. contra. assumption.
apply reg_running_rel.
- repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
assert(Hnd: gtype (gs (share habd)) @ (__addr_to_gidx z0) <> GRANULE_STATE_DATA). autounfold; omega.
repeat rewrite (relate_share_g_data _ _ id_share _ Hnd). grewrite.
simpl in *. red in Prop5. red in Prop3. red in Prop4.
repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
{ duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl; try assumption. }
{ duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl; try assumption. }
intros (ld & Hld & Hrel0). rewrite Hld.
clear id_share rel_secure invs.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C22. simpl_query_oracle' Hld.
repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try reflexivity.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; try assumption; autounfold in *.
+ constructor; simpl; try assumption.
- repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
assert(Hnd: gtype (gs (share habd)) @ (__addr_to_gidx z0) <> GRANULE_STATE_DATA). autounfold; omega.
repeat rewrite (relate_share_g_data _ _ id_share _ Hnd). grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try reflexivity.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; try assumption; autounfold in *.
+ constructor; simpl; try assumption.
- repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
assert(Hnd: gtype (gs (share habd)) @ (__addr_to_gidx z0) <> GRANULE_STATE_DATA). autounfold; omega.
repeat rewrite (relate_share_g_data _ _ id_share _ Hnd). grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try reflexivity.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; try assumption; autounfold in *.
+ constructor; simpl; try assumption.
- repeat (rewrite_sec_rel; grewrite; simpl_htarget; simpl).
repeat rewrite (relate_share_g_data _ _ id_share _ Hnd). grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; try assumption; autounfold in *.
+ constructor; simpl; try assumption.
- eexists; split. reflexivity.
constructor; simpl; assumption.
Qed.
Lemma smc_realm_destroy_security:
forall habd habd' labd rd_addr ret
(Hspec: smc_realm_destroy_spec rd_addr habd = Some (habd', ret))
(Hrel: relate_adt habd labd),
exists labd', smc_realm_destroy_spec rd_addr labd = Some (labd', ret) /\ relate_adt habd' labd'.
Proof.
Local Opaque peq ptr_eq.
intros. destruct Hrel.
unfold smc_realm_destroy_spec in *.
repeat autounfold in *.
rewrite_sec_rel.
simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec.
exploit (query_oracle_security habd r labd C3); try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel0). rewrite Hld.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C3. simpl_query_oracle' Hld.
repeat (rewrite_sec_rel; simpl_hyp Hspec; simpl in * ); extract_prop_dec; inv Hspec.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_share; auto.
+ constructor; simpl; try assumption; autounfold in *.
* intro gidx.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
auto.
* intro rd_gidx. repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. exploit rd_gcnt; try eassumption. eexists. split; eassumption.
intro T; inv T. intros. pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
intros. pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
intros. pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
* intro rd_gidx. repeat (destruct_zmap; simpl); try solve[intros; omega].
intros until b. intros.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?).
repeat (destruct_zmap; simpl); try solve[intros; omega].
srewrite. omega. srewrite. omega. srewrite. omega.
* intros rd_gidx rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. apply cur_running in running. srewrite. contra. assumption.
* intros rd_gidx rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. apply cur_running in running. srewrite. contra. assumption.
* intro rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
apply cur_running.
+ constructor; simpl; try assumption; autounfold in *.
* intro rd_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. exploit table_prop; try eassumption.
intros (Ha & Hb & Hc).
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
apply mem_rel; assumption.
* intros rd_gidx rec_gidx. autounfold.
repeat (destruct_zmap; simpl); try solve[intros; omega].
apply reg_not_run_rel.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
repeat (destruct_zmap; simpl); try solve[intros; omega].
apply reg_running_rel.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; try assumption.
+ constructor; simpl; try assumption.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; try assumption.
+ constructor; simpl; try assumption.
- inv Hspec. eexists; split. reflexivity.
constructor; simpl; assumption.
Qed.
Lemma smc_realm_activate_security:
forall habd habd' labd addr ret
(Hspec: smc_realm_activate_spec addr habd = Some (habd', ret))
(Hrel: relate_adt habd labd),
exists labd', smc_realm_activate_spec addr labd = Some (labd', ret) /\ relate_adt habd' labd'.
Proof.
intros. destruct Hrel.
unfold smc_realm_activate_spec in *.
repeat autounfold in *.
repeat (rewrite_sec_rel; simpl_hyp Hspec; simpl in * ); extract_prop_dec; inv Hspec.
- match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel0). rewrite Hld.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C3. simpl_query_oracle' Hld.
rewrite_sec_rel. simpl_htarget. grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. destruct_zmap; constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data s s0 id_share). reflexivity.
grewrite. autounfold. omega.
intros. rewrite (relate_share_g_regs s s0 id_share). reflexivity.
grewrite. autounfold. omega.
intros. rewrite (relate_share_g_data s s0 id_share). reflexivity. assumption.
intros. rewrite (relate_share_g_regs s s0 id_share). reflexivity. assumption.
+ constructor; simpl; try assumption; autounfold in *.
* intro gidx. destruct_zmap; simpl; auto.
* intro gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros. apply rec_rd in H. srewrite. omega. auto.
* intros rd_gidx. destruct_zmap; simpl.
intros until b. destruct_zmap; simpl. intros.
rewrite <- Heq in H. exploit (table_prop rd_gidx H ipa_gidx data_gidx); srewrite; try eassumption.
auto. apply table_prop; try assumption.
intros until b. destruct_zmap; simpl. intros.
exploit (table_prop rd_gidx H ipa_gidx data_gidx); srewrite; try eassumption. reflexivity.
auto. apply table_prop; try assumption.
* intros until rec_gidx. destruct_zmap; simpl.
destruct_zmap; simpl. intros; omega. apply tlb_prop; assumption.
destruct_zmap; simpl. intros; omega. apply tlb_prop; assumption.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega. apply running_not_new; assumption.
* intros rec_gidx. destruct_zmap; simpl. intros; omega. auto.
+ constructor; simpl; try assumption; autounfold in *.
* intro rd_gidx. destruct_zmap; simpl.
intros. rewrite <- Heq in *. exploit (mem_rel rd_gidx); try eassumption.
destruct_zmap; simpl.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega. auto.
intros. exploit (mem_rel rd_gidx); try eassumption.
destruct_zmap; simpl.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega. auto.
* intros rd_gidx rec_gidx. autounfold. destruct_zmap; simpl.
destruct_zmap. simpl. intros. omega. eapply reg_not_run_rel.
destruct_zmap. simpl. intros. omega. eapply reg_not_run_rel.
* intros until rec_gidx. destruct_zmap; simpl.
destruct_zmap; simpl. intros; omega. intros.
apply cur_running in running. srewrite. contra. assumption.
destruct_zmap; simpl. intros; omega. intros.
apply cur_running in running. srewrite. contra. assumption.
- match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel0). rewrite Hld.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C3. simpl_query_oracle' Hld.
rewrite_sec_rel. simpl_htarget. grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. destruct_zmap; constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data s s0 id_share). reflexivity.
grewrite. autounfold. omega.
intros. rewrite (relate_share_g_regs s s0 id_share). reflexivity.
grewrite. autounfold. omega.
intros. rewrite (relate_share_g_data s s0 id_share). reflexivity. assumption.
intros. rewrite (relate_share_g_regs s s0 id_share). reflexivity. assumption.
+ constructor; simpl; try assumption; autounfold in *.
* intro gidx. destruct_zmap; simpl; auto.
* intro gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros. apply rec_rd in H. srewrite. omega. auto.
* intros rd_gidx. destruct_zmap; simpl.
intros until b. destruct_zmap; simpl. intros.
rewrite <- Heq in H. exploit (table_prop rd_gidx H ipa_gidx data_gidx); srewrite; try eassumption.
auto. apply table_prop; try assumption.
intros until b. destruct_zmap; simpl. intros.
exploit (table_prop rd_gidx H ipa_gidx data_gidx); srewrite; try eassumption. reflexivity.
auto. apply table_prop; try assumption.
* intros until rec_gidx. destruct_zmap; simpl.
destruct_zmap; simpl. intros; omega. apply tlb_prop; assumption.
destruct_zmap; simpl. intros; omega. apply tlb_prop; assumption.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega. apply running_not_new; assumption.
* intros rec_gidx. destruct_zmap; simpl. intros; omega. auto.
+ constructor; simpl; try assumption; autounfold in *.
* intro rd_gidx. destruct_zmap; simpl.
intros. rewrite <- Heq in *. exploit (mem_rel rd_gidx); try eassumption.
destruct_zmap; simpl.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega. auto.
intros. exploit (mem_rel rd_gidx); try eassumption.
destruct_zmap; simpl.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?). srewrite. omega. auto.
* intros rd_gidx rec_gidx. autounfold. destruct_zmap; simpl.
destruct_zmap. simpl. intros. omega. eapply reg_not_run_rel.
destruct_zmap. simpl. intros. omega. eapply reg_not_run_rel.
* intros until rec_gidx. destruct_zmap; simpl.
destruct_zmap; simpl. intros; omega. intros.
apply cur_running in running. srewrite. contra. assumption.
destruct_zmap; simpl. intros; omega. intros.
apply cur_running in running. srewrite. contra. assumption.
- match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel). rewrite Hld.
destruct Hrel as (id_share & invs & rel_secure).
simpl_query_oracle' C3. simpl_query_oracle' Hld.
rewrite_sec_rel. simpl_htarget. grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_share. assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_priv. assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try assumption.
+ constructor; simpl; assumption.
- match goal with
| [H: query_oracle ?hd = Some ?hd' |- context[query_oracle ?ld]] =>
exploit (query_oracle_security hd hd' ld H)
end; try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel). rewrite Hld.
destruct Hrel as (id_share & invs & rel_secure).
simpl_query_oracle' C3. simpl_query_oracle' Hld.
rewrite_sec_rel. simpl_htarget. grewrite.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_share. assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct id_priv. assumption.
+ simpl; constructor; simpl; rewrite_sec_rel; try assumption.
+ constructor; simpl; assumption.
- eexists; split. reflexivity.
constructor; simpl; assumption.
Qed.
Lemma smc_rec_create_security:
forall habd habd' labd rec_addr rd_addr mpidr rec_param_addr ret
(Hspec: smc_rec_create_spec rec_addr rd_addr mpidr rec_param_addr habd = Some (habd', ret))
(Hrel: relate_adt habd labd) (rmm_run: cur_rec (priv habd) = None),
exists labd', smc_rec_create_spec rec_addr rd_addr mpidr rec_param_addr labd = Some (labd', ret) /\ relate_adt habd' labd'.
Proof.
intros. destruct Hrel.
unfold smc_rec_create_spec in *. repeat autounfold in *.
simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec.
simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec.
simpl_hyp Hspec. exploit (query_oracle_security habd r labd C9); try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel0). rewrite Hld.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C9. simpl_query_oracle' Hld.
repeat (rewrite_sec_rel; simpl_hyp Hspec; simpl in * ); extract_prop_dec; inv Hspec;
repeat (grewrite; try simpl_htarget; simpl).
- rewrite (relate_share_g_data _ _ id_share). grewrite.
rewrite (relate_share_g_data _ _ id_share). simpl_htarget.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_regs _ _ id_share). reflexivity.
grewrite. autounfold; omega.
destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data _ _ id_share). reflexivity.
grewrite. autounfold; omega.
intros. rewrite (relate_share_g_regs _ _ id_share). reflexivity.
grewrite. autounfold; omega.
destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data _ _ id_share). reflexivity.
grewrite. autounfold; omega.
intros. rewrite (relate_share_g_regs _ _ id_share). reflexivity.
grewrite. autounfold; omega. unfold init_grec. simpl.
destruct id_share; auto.
+ simpl; constructor; simpl; rewrite_sec_rel; try reflexivity.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; try assumption; autounfold in *.
* intro gidx.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
auto.
* intro rd_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. destruct_zmap; simpl.
symmetry in Heq2. srewrite. rewrite ZMap.gss. simpl. intros. assumption.
rewrite ZMap.gss. simpl; intros. assumption.
destruct_zmap; simpl.
intros. pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
destruct_zmap; simpl.
intros. pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
destruct_zmap; simpl.
intros. pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
auto.
* intro rd_gidx. destruct_zmap; simpl. intros; omega.
destruct_zmap; simpl. intros. rewrite <- Heq0 in *.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?).
destruct_zmap; simpl. srewrite; omega.
destruct_zmap; simpl. srewrite; omega.
destruct_zmap; simpl. srewrite; omega.
eapply table_prop; eassumption.
destruct_zmap; simpl. intros; omega. intros.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?).
destruct_zmap; simpl. srewrite; omega.
destruct_zmap; simpl. srewrite; omega.
destruct_zmap; simpl. srewrite; omega.
eapply table_prop; eassumption.
* intros rd_gidx rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
exploit (delegate_zero s (__addr_to_gidx z)). assumption.
intros (Ha & Hb). intros. srewrite. inv running.
intros. rewrite <- Heq0 in *.
eapply tlb_prop; eassumption. eapply tlb_prop; eassumption.
* intros rd_gidx rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. exploit (delegate_zero s (__addr_to_gidx z)). assumption.
intros (Ha & Hb). intros. srewrite. inv running.
intros. rewrite <- Heq0 in *.
eapply running_not_new; eassumption. eapply running_not_new; eassumption.
* intro rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. exploit (delegate_zero s (__addr_to_gidx z)). assumption.
intros (Ha & Hb). intros. srewrite. inv running.
apply cur_running.
+ constructor; simpl; try assumption; autounfold in *.
* intro rd_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. exploit table_prop; try eassumption. intros (Ha & Hb & Hc).
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
apply mem_rel; assumption.
intros. exploit table_prop; try eassumption. intros (Ha & Hb & Hc).
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
apply mem_rel; assumption.
* intros rd_gidx rec_gidx. autounfold.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. erewrite new_decl_regs. simpl.
intros. exploit (delegate_zero s (__addr_to_gidx z)). assumption.
intros (Ha & Hb).
intros. exploit (delegate_zero s0 (__addr_to_gidx z)). rewrite_sec_rel. assumption.
intros (Ha' & Hb'). intros. srewrite. reflexivity.
assumption. bool_rel_all. assumption.
rewrite <- Heq0. apply reg_not_run_rel. apply reg_not_run_rel.
* intros until rec_gidx. destruct_zmap; simpl. intros; omega.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. exploit (delegate_zero s (__addr_to_gidx z)). assumption.
intros (Ha & Hb). intros. srewrite. inv running.
intros. apply cur_running in running. srewrite. contra. assumption.
intros. apply cur_running in running. srewrite. contra. assumption.
+ autounfold. bool_rel_all. omega.
+ autounfold. bool_rel_all. omega.
- rewrite (relate_share_g_data _ _ id_share). grewrite.
rewrite (relate_share_g_data _ _ id_share). simpl_htarget.
eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
constructor; simpl; rewrite_sec_rel; try reflexivity.
+ constructor; simpl; try assumption; autounfold in *.
+ constructor; simpl; try assumption.
+ autounfold. bool_rel_all. omega.
+ autounfold. bool_rel_all. omega.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; try assumption.
+ constructor; simpl; try assumption.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; try assumption.
+ constructor; simpl; try assumption.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; try assumption.
+ constructor; simpl; try assumption.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; try assumption.
+ constructor; simpl; try assumption.
- rewrite_sec_rel. extract_prop_dec. simpl_htarget. inv Hspec.
eexists; split. reflexivity. constructor; assumption.
Qed.
Lemma smc_rec_destroy_security:
forall habd habd' labd rec_addr ret
(Hspec: smc_rec_destroy_spec rec_addr habd = Some (habd', ret))
(Hrel: relate_adt habd labd),
exists labd', smc_rec_destroy_spec rec_addr labd = Some (labd', ret) /\ relate_adt habd' labd'.
Proof.
Local Opaque peq ptr_eq.
intros. destruct Hrel.
unfold smc_rec_destroy_spec in *.
repeat autounfold in *.
rewrite_sec_rel.
simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec. simpl_hyp Hspec.
exploit (query_oracle_security habd r labd C3); try assumption.
clear id_share rel_secure invs.
intros (ld & Hld & Hrel0). rewrite Hld.
destruct Hrel0 as (id_share & invs & rel_secure).
simpl_query_oracle' C3. simpl_query_oracle' Hld.
repeat (rewrite_sec_rel; simpl_hyp Hspec; simpl in * ); extract_prop_dec; inv Hspec.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data _ _ id_share). reflexivity.
grewrite. autounfold; omega.
intros. rewrite (relate_share_g_regs _ _ id_share). reflexivity.
grewrite. autounfold; omega.
destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
destruct_zmap; simpl.
constructor; simpl; rewrite_sec_rel; try reflexivity.
intros. rewrite (relate_share_g_data _ _ id_share). reflexivity.
grewrite. autounfold; omega.
intros. rewrite (relate_share_g_regs _ _ id_share). reflexivity.
grewrite. autounfold; omega.
destruct id_share; auto.
+ constructor; simpl; try assumption; autounfold in *.
* intro gidx.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
destruct_zmap; simpl. intros. apply gpt_false_ns in H. srewrite. omega.
auto.
* intro rd_gidx. repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
intros. pose proof (rec_rd rd_gidx). apply H0 in H. srewrite. omega.
auto.
* intro rd_gidx. repeat (destruct_zmap; simpl); try solve[intros; omega].
intros until b. intros.
rewrite <- Heq in *. exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?).
repeat (destruct_zmap; simpl); try solve[intros; omega].
srewrite. omega. srewrite. omega. srewrite. omega.
intros until b. intros.
exploit (table_prop rd_gidx); try eassumption.
intros (? & ? & ?).
repeat (destruct_zmap; simpl); try solve[intros; omega].
srewrite. omega. srewrite. omega. srewrite. omega.
* intros rd_gidx rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. apply cur_running in running. srewrite. contra. assumption.
apply tlb_prop.
* intros rd_gidx rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. apply cur_running in running. srewrite. contra. assumption.
apply running_not_new.
* intro rec_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
apply cur_running.
+ constructor; simpl; try assumption; autounfold in *.
* intro rd_gidx.
repeat (destruct_zmap; simpl); try solve[intros; omega].
intros. rewrite <- Heq in *. exploit table_prop; try eassumption.
intros (Ha & Hb & Hc).
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
apply mem_rel; assumption.
intros. exploit table_prop; try eassumption.
intros (Ha & Hb & Hc).
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
destruct_zmap; simpl. srewrite. omega.
apply mem_rel; assumption.
* intros rd_gidx rec_gidx. autounfold.
repeat (destruct_zmap; simpl); try solve[intros; omega].
apply reg_not_run_rel. apply reg_not_run_rel.
* intros until rec_gidx. destruct_zmap; simpl.
repeat (destruct_zmap; simpl); try solve[intros; omega].
apply reg_running_rel.
repeat (destruct_zmap; simpl); try solve[intros; omega].
apply reg_running_rel.
- eexists; split. reflexivity.
duplicate invs. destruct D. duplicate rel_secure. destruct D. simpl in *.
constructor; simpl in *; try assumption.
+ constructor; simpl; try assumption.
+ constructor; simpl; try assumption.
- inv Hspec. eexists; split. reflexivity.
constructor; simpl; assumption.
Qed.