forked from rems-project/sail
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Cheri_lemmas.thy
1270 lines (961 loc) · 64.3 KB
/
Cheri_lemmas.thy
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
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
theory Cheri_lemmas
imports
Sail.Sail2_values_lemmas
Sail.Sail2_state_lemmas
Cheri
begin
abbreviation liftS ("\<lbrakk>_\<rbrakk>\<^sub>S") where "liftS \<equiv> liftState (get_regval, set_regval)"
lemmas register_defs = get_regval_def set_regval_def instCount_ref_def CapCause_ref_def KDC_ref_def
KR2C_ref_def KR1C_ref_def CTLSP_ref_def CTLSU_ref_def C31_ref_def C30_ref_def C29_ref_def
C28_ref_def C27_ref_def C26_ref_def C25_ref_def C24_ref_def C23_ref_def C22_ref_def C21_ref_def
C20_ref_def C19_ref_def C18_ref_def C17_ref_def C16_ref_def C15_ref_def C14_ref_def C13_ref_def
C12_ref_def C11_ref_def C10_ref_def C09_ref_def C08_ref_def C07_ref_def C06_ref_def C05_ref_def
C04_ref_def C03_ref_def C02_ref_def C01_ref_def DDC_ref_def inCCallDelay_ref_def nextPCC_ref_def
delayedPCC_ref_def PCC_ref_def KCC_ref_def EPCC_ref_def UART_RVALID_ref_def UART_RDATA_ref_def
UART_WRITTEN_ref_def UART_WDATA_ref_def GPR_ref_def LO_ref_def HI_ref_def delayedPC_ref_def
inBranchDelay_ref_def branchPending_ref_def CP0Status_ref_def CP0ConfigK0_ref_def
CP0UserLocal_ref_def CP0HWREna_ref_def CP0Count_ref_def CP0BadVAddr_ref_def CP0LLAddr_ref_def
CP0LLBit_ref_def CP0ErrorEPC_ref_def CP0EPC_ref_def CP0Cause_ref_def CP0Compare_ref_def
TLBEntry63_ref_def TLBEntry62_ref_def TLBEntry61_ref_def TLBEntry60_ref_def TLBEntry59_ref_def
TLBEntry58_ref_def TLBEntry57_ref_def TLBEntry56_ref_def TLBEntry55_ref_def TLBEntry54_ref_def
TLBEntry53_ref_def TLBEntry52_ref_def TLBEntry51_ref_def TLBEntry50_ref_def TLBEntry49_ref_def
TLBEntry48_ref_def TLBEntry47_ref_def TLBEntry46_ref_def TLBEntry45_ref_def TLBEntry44_ref_def
TLBEntry43_ref_def TLBEntry42_ref_def TLBEntry41_ref_def TLBEntry40_ref_def TLBEntry39_ref_def
TLBEntry38_ref_def TLBEntry37_ref_def TLBEntry36_ref_def TLBEntry35_ref_def TLBEntry34_ref_def
TLBEntry33_ref_def TLBEntry32_ref_def TLBEntry31_ref_def TLBEntry30_ref_def TLBEntry29_ref_def
TLBEntry28_ref_def TLBEntry27_ref_def TLBEntry26_ref_def TLBEntry25_ref_def TLBEntry24_ref_def
TLBEntry23_ref_def TLBEntry22_ref_def TLBEntry21_ref_def TLBEntry20_ref_def TLBEntry19_ref_def
TLBEntry18_ref_def TLBEntry17_ref_def TLBEntry16_ref_def TLBEntry15_ref_def TLBEntry14_ref_def
TLBEntry13_ref_def TLBEntry12_ref_def TLBEntry11_ref_def TLBEntry10_ref_def TLBEntry09_ref_def
TLBEntry08_ref_def TLBEntry07_ref_def TLBEntry06_ref_def TLBEntry05_ref_def TLBEntry04_ref_def
TLBEntry03_ref_def TLBEntry02_ref_def TLBEntry01_ref_def TLBEntry00_ref_def TLBXContext_ref_def
TLBEntryHi_ref_def TLBWired_ref_def TLBPageMask_ref_def TLBContext_ref_def TLBEntryLo1_ref_def
TLBEntryLo0_ref_def TLBRandom_ref_def TLBIndex_ref_def TLBProbe_ref_def nextPC_ref_def PC_ref_def
lemma regval_CapCauseReg[simp]:
"CapCauseReg_of_regval (regval_of_CapCauseReg v) = Some v"
by (auto simp: regval_of_CapCauseReg_def)
lemma regval_CauseReg[simp]:
"CauseReg_of_regval (regval_of_CauseReg v) = Some v"
by (auto simp: regval_of_CauseReg_def)
lemma regval_ContextReg[simp]:
"ContextReg_of_regval (regval_of_ContextReg v) = Some v"
by (auto simp: regval_of_ContextReg_def)
lemma regval_StatusReg[simp]:
"StatusReg_of_regval (regval_of_StatusReg v) = Some v"
by (auto simp: regval_of_StatusReg_def)
lemma regval_TLBEntry[simp]:
"TLBEntry_of_regval (regval_of_TLBEntry v) = Some v"
by (auto simp: regval_of_TLBEntry_def)
lemma regval_TLBEntryHiReg[simp]:
"TLBEntryHiReg_of_regval (regval_of_TLBEntryHiReg v) = Some v"
by (auto simp: regval_of_TLBEntryHiReg_def)
lemma regval_TLBEntryLoReg[simp]:
"TLBEntryLoReg_of_regval (regval_of_TLBEntryLoReg v) = Some v"
by (auto simp: regval_of_TLBEntryLoReg_def)
lemma regval_XContextReg[simp]:
"XContextReg_of_regval (regval_of_XContextReg v) = Some v"
by (auto simp: regval_of_XContextReg_def)
lemma regval_int[simp]:
"int_of_regval (regval_of_int v) = Some v"
by (auto simp: regval_of_int_def)
lemma regval_vector_16_dec_bit[simp]:
"vector_16_dec_bit_of_regval (regval_of_vector_16_dec_bit v) = Some v"
by (auto simp: regval_of_vector_16_dec_bit_def)
lemma regval_vector_1_dec_bit[simp]:
"vector_1_dec_bit_of_regval (regval_of_vector_1_dec_bit v) = Some v"
by (auto simp: regval_of_vector_1_dec_bit_def)
lemma regval_vector_257_dec_bit[simp]:
"vector_257_dec_bit_of_regval (regval_of_vector_257_dec_bit v) = Some v"
by (auto simp: regval_of_vector_257_dec_bit_def)
lemma regval_vector_32_dec_bit[simp]:
"vector_32_dec_bit_of_regval (regval_of_vector_32_dec_bit v) = Some v"
by (auto simp: regval_of_vector_32_dec_bit_def)
lemma regval_vector_3_dec_bit[simp]:
"vector_3_dec_bit_of_regval (regval_of_vector_3_dec_bit v) = Some v"
by (auto simp: regval_of_vector_3_dec_bit_def)
lemma regval_vector_64_dec_bit[simp]:
"vector_64_dec_bit_of_regval (regval_of_vector_64_dec_bit v) = Some v"
by (auto simp: regval_of_vector_64_dec_bit_def)
lemma regval_vector_6_dec_bit[simp]:
"vector_6_dec_bit_of_regval (regval_of_vector_6_dec_bit v) = Some v"
by (auto simp: regval_of_vector_6_dec_bit_def)
lemma regval_vector_8_dec_bit[simp]:
"vector_8_dec_bit_of_regval (regval_of_vector_8_dec_bit v) = Some v"
by (auto simp: regval_of_vector_8_dec_bit_def)
lemma vector_of_rv_rv_of_vector[simp]:
assumes "\<And>v. of_rv (rv_of v) = Some v"
shows "vector_of_regval of_rv (regval_of_vector rv_of len is_inc v) = Some v"
proof -
from assms have "of_rv \<circ> rv_of = Some" by auto
then show ?thesis by (auto simp: vector_of_regval_def regval_of_vector_def)
qed
lemma option_of_rv_rv_of_option[simp]:
assumes "\<And>v. of_rv (rv_of v) = Some v"
shows "option_of_regval of_rv (regval_of_option rv_of v) = Some v"
using assms by (cases v) (auto simp: option_of_regval_def regval_of_option_def)
lemma list_of_rv_rv_of_list[simp]:
assumes "\<And>v. of_rv (rv_of v) = Some v"
shows "list_of_regval of_rv (regval_of_list rv_of v) = Some v"
proof -
from assms have "of_rv \<circ> rv_of = Some" by auto
with assms show ?thesis by (induction v) (auto simp: list_of_regval_def regval_of_list_def)
qed
lemma liftS_read_reg_instCount[liftState_simp]:
"\<lbrakk>read_reg instCount_ref\<rbrakk>\<^sub>S = readS (instCount \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_instCount[liftState_simp]:
"\<lbrakk>write_reg instCount_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (instCount_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CapCause[liftState_simp]:
"\<lbrakk>read_reg CapCause_ref\<rbrakk>\<^sub>S = readS (CapCause \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CapCause[liftState_simp]:
"\<lbrakk>write_reg CapCause_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CapCause_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_KDC[liftState_simp]:
"\<lbrakk>read_reg KDC_ref\<rbrakk>\<^sub>S = readS (KDC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_KDC[liftState_simp]:
"\<lbrakk>write_reg KDC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (KDC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_KR2C[liftState_simp]:
"\<lbrakk>read_reg KR2C_ref\<rbrakk>\<^sub>S = readS (KR2C \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_KR2C[liftState_simp]:
"\<lbrakk>write_reg KR2C_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (KR2C_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_KR1C[liftState_simp]:
"\<lbrakk>read_reg KR1C_ref\<rbrakk>\<^sub>S = readS (KR1C \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_KR1C[liftState_simp]:
"\<lbrakk>write_reg KR1C_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (KR1C_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CTLSP[liftState_simp]:
"\<lbrakk>read_reg CTLSP_ref\<rbrakk>\<^sub>S = readS (CTLSP \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CTLSP[liftState_simp]:
"\<lbrakk>write_reg CTLSP_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CTLSP_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CTLSU[liftState_simp]:
"\<lbrakk>read_reg CTLSU_ref\<rbrakk>\<^sub>S = readS (CTLSU \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CTLSU[liftState_simp]:
"\<lbrakk>write_reg CTLSU_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CTLSU_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C31[liftState_simp]:
"\<lbrakk>read_reg C31_ref\<rbrakk>\<^sub>S = readS (C31 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C31[liftState_simp]:
"\<lbrakk>write_reg C31_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C31_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C30[liftState_simp]:
"\<lbrakk>read_reg C30_ref\<rbrakk>\<^sub>S = readS (C30 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C30[liftState_simp]:
"\<lbrakk>write_reg C30_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C30_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C29[liftState_simp]:
"\<lbrakk>read_reg C29_ref\<rbrakk>\<^sub>S = readS (C29 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C29[liftState_simp]:
"\<lbrakk>write_reg C29_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C29_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C28[liftState_simp]:
"\<lbrakk>read_reg C28_ref\<rbrakk>\<^sub>S = readS (C28 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C28[liftState_simp]:
"\<lbrakk>write_reg C28_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C28_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C27[liftState_simp]:
"\<lbrakk>read_reg C27_ref\<rbrakk>\<^sub>S = readS (C27 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C27[liftState_simp]:
"\<lbrakk>write_reg C27_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C27_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C26[liftState_simp]:
"\<lbrakk>read_reg C26_ref\<rbrakk>\<^sub>S = readS (C26 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C26[liftState_simp]:
"\<lbrakk>write_reg C26_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C26_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C25[liftState_simp]:
"\<lbrakk>read_reg C25_ref\<rbrakk>\<^sub>S = readS (C25 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C25[liftState_simp]:
"\<lbrakk>write_reg C25_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C25_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C24[liftState_simp]:
"\<lbrakk>read_reg C24_ref\<rbrakk>\<^sub>S = readS (C24 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C24[liftState_simp]:
"\<lbrakk>write_reg C24_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C24_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C23[liftState_simp]:
"\<lbrakk>read_reg C23_ref\<rbrakk>\<^sub>S = readS (C23 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C23[liftState_simp]:
"\<lbrakk>write_reg C23_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C23_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C22[liftState_simp]:
"\<lbrakk>read_reg C22_ref\<rbrakk>\<^sub>S = readS (C22 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C22[liftState_simp]:
"\<lbrakk>write_reg C22_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C22_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C21[liftState_simp]:
"\<lbrakk>read_reg C21_ref\<rbrakk>\<^sub>S = readS (C21 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C21[liftState_simp]:
"\<lbrakk>write_reg C21_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C21_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C20[liftState_simp]:
"\<lbrakk>read_reg C20_ref\<rbrakk>\<^sub>S = readS (C20 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C20[liftState_simp]:
"\<lbrakk>write_reg C20_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C20_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C19[liftState_simp]:
"\<lbrakk>read_reg C19_ref\<rbrakk>\<^sub>S = readS (C19 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C19[liftState_simp]:
"\<lbrakk>write_reg C19_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C19_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C18[liftState_simp]:
"\<lbrakk>read_reg C18_ref\<rbrakk>\<^sub>S = readS (C18 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C18[liftState_simp]:
"\<lbrakk>write_reg C18_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C18_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C17[liftState_simp]:
"\<lbrakk>read_reg C17_ref\<rbrakk>\<^sub>S = readS (C17 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C17[liftState_simp]:
"\<lbrakk>write_reg C17_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C17_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C16[liftState_simp]:
"\<lbrakk>read_reg C16_ref\<rbrakk>\<^sub>S = readS (C16 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C16[liftState_simp]:
"\<lbrakk>write_reg C16_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C16_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C15[liftState_simp]:
"\<lbrakk>read_reg C15_ref\<rbrakk>\<^sub>S = readS (C15 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C15[liftState_simp]:
"\<lbrakk>write_reg C15_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C15_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C14[liftState_simp]:
"\<lbrakk>read_reg C14_ref\<rbrakk>\<^sub>S = readS (C14 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C14[liftState_simp]:
"\<lbrakk>write_reg C14_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C14_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C13[liftState_simp]:
"\<lbrakk>read_reg C13_ref\<rbrakk>\<^sub>S = readS (C13 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C13[liftState_simp]:
"\<lbrakk>write_reg C13_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C13_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C12[liftState_simp]:
"\<lbrakk>read_reg C12_ref\<rbrakk>\<^sub>S = readS (C12 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C12[liftState_simp]:
"\<lbrakk>write_reg C12_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C12_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C11[liftState_simp]:
"\<lbrakk>read_reg C11_ref\<rbrakk>\<^sub>S = readS (C11 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C11[liftState_simp]:
"\<lbrakk>write_reg C11_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C11_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C10[liftState_simp]:
"\<lbrakk>read_reg C10_ref\<rbrakk>\<^sub>S = readS (C10 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C10[liftState_simp]:
"\<lbrakk>write_reg C10_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C10_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C09[liftState_simp]:
"\<lbrakk>read_reg C09_ref\<rbrakk>\<^sub>S = readS (C09 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C09[liftState_simp]:
"\<lbrakk>write_reg C09_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C09_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C08[liftState_simp]:
"\<lbrakk>read_reg C08_ref\<rbrakk>\<^sub>S = readS (C08 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C08[liftState_simp]:
"\<lbrakk>write_reg C08_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C08_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C07[liftState_simp]:
"\<lbrakk>read_reg C07_ref\<rbrakk>\<^sub>S = readS (C07 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C07[liftState_simp]:
"\<lbrakk>write_reg C07_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C07_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C06[liftState_simp]:
"\<lbrakk>read_reg C06_ref\<rbrakk>\<^sub>S = readS (C06 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C06[liftState_simp]:
"\<lbrakk>write_reg C06_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C06_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C05[liftState_simp]:
"\<lbrakk>read_reg C05_ref\<rbrakk>\<^sub>S = readS (C05 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C05[liftState_simp]:
"\<lbrakk>write_reg C05_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C05_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C04[liftState_simp]:
"\<lbrakk>read_reg C04_ref\<rbrakk>\<^sub>S = readS (C04 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C04[liftState_simp]:
"\<lbrakk>write_reg C04_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C04_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C03[liftState_simp]:
"\<lbrakk>read_reg C03_ref\<rbrakk>\<^sub>S = readS (C03 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C03[liftState_simp]:
"\<lbrakk>write_reg C03_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C03_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C02[liftState_simp]:
"\<lbrakk>read_reg C02_ref\<rbrakk>\<^sub>S = readS (C02 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C02[liftState_simp]:
"\<lbrakk>write_reg C02_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C02_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_C01[liftState_simp]:
"\<lbrakk>read_reg C01_ref\<rbrakk>\<^sub>S = readS (C01 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_C01[liftState_simp]:
"\<lbrakk>write_reg C01_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (C01_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_DDC[liftState_simp]:
"\<lbrakk>read_reg DDC_ref\<rbrakk>\<^sub>S = readS (DDC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_DDC[liftState_simp]:
"\<lbrakk>write_reg DDC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (DDC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_inCCallDelay[liftState_simp]:
"\<lbrakk>read_reg inCCallDelay_ref\<rbrakk>\<^sub>S = readS (inCCallDelay \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_inCCallDelay[liftState_simp]:
"\<lbrakk>write_reg inCCallDelay_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (inCCallDelay_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_nextPCC[liftState_simp]:
"\<lbrakk>read_reg nextPCC_ref\<rbrakk>\<^sub>S = readS (nextPCC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_nextPCC[liftState_simp]:
"\<lbrakk>write_reg nextPCC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (nextPCC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_delayedPCC[liftState_simp]:
"\<lbrakk>read_reg delayedPCC_ref\<rbrakk>\<^sub>S = readS (delayedPCC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_delayedPCC[liftState_simp]:
"\<lbrakk>write_reg delayedPCC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (delayedPCC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_PCC[liftState_simp]:
"\<lbrakk>read_reg PCC_ref\<rbrakk>\<^sub>S = readS (PCC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_PCC[liftState_simp]:
"\<lbrakk>write_reg PCC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (PCC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_KCC[liftState_simp]:
"\<lbrakk>read_reg KCC_ref\<rbrakk>\<^sub>S = readS (KCC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_KCC[liftState_simp]:
"\<lbrakk>write_reg KCC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (KCC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_EPCC[liftState_simp]:
"\<lbrakk>read_reg EPCC_ref\<rbrakk>\<^sub>S = readS (EPCC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_EPCC[liftState_simp]:
"\<lbrakk>write_reg EPCC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (EPCC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_UART_RVALID[liftState_simp]:
"\<lbrakk>read_reg UART_RVALID_ref\<rbrakk>\<^sub>S = readS (UART_RVALID \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_UART_RVALID[liftState_simp]:
"\<lbrakk>write_reg UART_RVALID_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (UART_RVALID_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_UART_RDATA[liftState_simp]:
"\<lbrakk>read_reg UART_RDATA_ref\<rbrakk>\<^sub>S = readS (UART_RDATA \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_UART_RDATA[liftState_simp]:
"\<lbrakk>write_reg UART_RDATA_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (UART_RDATA_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_UART_WRITTEN[liftState_simp]:
"\<lbrakk>read_reg UART_WRITTEN_ref\<rbrakk>\<^sub>S = readS (UART_WRITTEN \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_UART_WRITTEN[liftState_simp]:
"\<lbrakk>write_reg UART_WRITTEN_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (UART_WRITTEN_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_UART_WDATA[liftState_simp]:
"\<lbrakk>read_reg UART_WDATA_ref\<rbrakk>\<^sub>S = readS (UART_WDATA \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_UART_WDATA[liftState_simp]:
"\<lbrakk>write_reg UART_WDATA_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (UART_WDATA_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_GPR[liftState_simp]:
"\<lbrakk>read_reg GPR_ref\<rbrakk>\<^sub>S = readS (GPR \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_GPR[liftState_simp]:
"\<lbrakk>write_reg GPR_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (GPR_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_LO[liftState_simp]:
"\<lbrakk>read_reg LO_ref\<rbrakk>\<^sub>S = readS (LO \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_LO[liftState_simp]:
"\<lbrakk>write_reg LO_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (LO_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_HI[liftState_simp]:
"\<lbrakk>read_reg HI_ref\<rbrakk>\<^sub>S = readS (HI \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_HI[liftState_simp]:
"\<lbrakk>write_reg HI_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (HI_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_delayedPC[liftState_simp]:
"\<lbrakk>read_reg delayedPC_ref\<rbrakk>\<^sub>S = readS (delayedPC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_delayedPC[liftState_simp]:
"\<lbrakk>write_reg delayedPC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (delayedPC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_inBranchDelay[liftState_simp]:
"\<lbrakk>read_reg inBranchDelay_ref\<rbrakk>\<^sub>S = readS (inBranchDelay \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_inBranchDelay[liftState_simp]:
"\<lbrakk>write_reg inBranchDelay_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (inBranchDelay_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_branchPending[liftState_simp]:
"\<lbrakk>read_reg branchPending_ref\<rbrakk>\<^sub>S = readS (branchPending \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_branchPending[liftState_simp]:
"\<lbrakk>write_reg branchPending_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (branchPending_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0Status[liftState_simp]:
"\<lbrakk>read_reg CP0Status_ref\<rbrakk>\<^sub>S = readS (CP0Status \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0Status[liftState_simp]:
"\<lbrakk>write_reg CP0Status_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0Status_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0ConfigK0[liftState_simp]:
"\<lbrakk>read_reg CP0ConfigK0_ref\<rbrakk>\<^sub>S = readS (CP0ConfigK0 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0ConfigK0[liftState_simp]:
"\<lbrakk>write_reg CP0ConfigK0_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0ConfigK0_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0UserLocal[liftState_simp]:
"\<lbrakk>read_reg CP0UserLocal_ref\<rbrakk>\<^sub>S = readS (CP0UserLocal \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0UserLocal[liftState_simp]:
"\<lbrakk>write_reg CP0UserLocal_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0UserLocal_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0HWREna[liftState_simp]:
"\<lbrakk>read_reg CP0HWREna_ref\<rbrakk>\<^sub>S = readS (CP0HWREna \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0HWREna[liftState_simp]:
"\<lbrakk>write_reg CP0HWREna_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0HWREna_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0Count[liftState_simp]:
"\<lbrakk>read_reg CP0Count_ref\<rbrakk>\<^sub>S = readS (CP0Count \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0Count[liftState_simp]:
"\<lbrakk>write_reg CP0Count_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0Count_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0BadVAddr[liftState_simp]:
"\<lbrakk>read_reg CP0BadVAddr_ref\<rbrakk>\<^sub>S = readS (CP0BadVAddr \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0BadVAddr[liftState_simp]:
"\<lbrakk>write_reg CP0BadVAddr_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0BadVAddr_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0LLAddr[liftState_simp]:
"\<lbrakk>read_reg CP0LLAddr_ref\<rbrakk>\<^sub>S = readS (CP0LLAddr \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0LLAddr[liftState_simp]:
"\<lbrakk>write_reg CP0LLAddr_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0LLAddr_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0LLBit[liftState_simp]:
"\<lbrakk>read_reg CP0LLBit_ref\<rbrakk>\<^sub>S = readS (CP0LLBit \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0LLBit[liftState_simp]:
"\<lbrakk>write_reg CP0LLBit_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0LLBit_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0ErrorEPC[liftState_simp]:
"\<lbrakk>read_reg CP0ErrorEPC_ref\<rbrakk>\<^sub>S = readS (CP0ErrorEPC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0ErrorEPC[liftState_simp]:
"\<lbrakk>write_reg CP0ErrorEPC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0ErrorEPC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0EPC[liftState_simp]:
"\<lbrakk>read_reg CP0EPC_ref\<rbrakk>\<^sub>S = readS (CP0EPC \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0EPC[liftState_simp]:
"\<lbrakk>write_reg CP0EPC_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0EPC_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0Cause[liftState_simp]:
"\<lbrakk>read_reg CP0Cause_ref\<rbrakk>\<^sub>S = readS (CP0Cause \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0Cause[liftState_simp]:
"\<lbrakk>write_reg CP0Cause_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0Cause_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_CP0Compare[liftState_simp]:
"\<lbrakk>read_reg CP0Compare_ref\<rbrakk>\<^sub>S = readS (CP0Compare \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_CP0Compare[liftState_simp]:
"\<lbrakk>write_reg CP0Compare_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (CP0Compare_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry63[liftState_simp]:
"\<lbrakk>read_reg TLBEntry63_ref\<rbrakk>\<^sub>S = readS (TLBEntry63 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry63[liftState_simp]:
"\<lbrakk>write_reg TLBEntry63_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry63_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry62[liftState_simp]:
"\<lbrakk>read_reg TLBEntry62_ref\<rbrakk>\<^sub>S = readS (TLBEntry62 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry62[liftState_simp]:
"\<lbrakk>write_reg TLBEntry62_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry62_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry61[liftState_simp]:
"\<lbrakk>read_reg TLBEntry61_ref\<rbrakk>\<^sub>S = readS (TLBEntry61 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry61[liftState_simp]:
"\<lbrakk>write_reg TLBEntry61_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry61_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry60[liftState_simp]:
"\<lbrakk>read_reg TLBEntry60_ref\<rbrakk>\<^sub>S = readS (TLBEntry60 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry60[liftState_simp]:
"\<lbrakk>write_reg TLBEntry60_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry60_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry59[liftState_simp]:
"\<lbrakk>read_reg TLBEntry59_ref\<rbrakk>\<^sub>S = readS (TLBEntry59 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry59[liftState_simp]:
"\<lbrakk>write_reg TLBEntry59_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry59_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry58[liftState_simp]:
"\<lbrakk>read_reg TLBEntry58_ref\<rbrakk>\<^sub>S = readS (TLBEntry58 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry58[liftState_simp]:
"\<lbrakk>write_reg TLBEntry58_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry58_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry57[liftState_simp]:
"\<lbrakk>read_reg TLBEntry57_ref\<rbrakk>\<^sub>S = readS (TLBEntry57 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry57[liftState_simp]:
"\<lbrakk>write_reg TLBEntry57_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry57_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry56[liftState_simp]:
"\<lbrakk>read_reg TLBEntry56_ref\<rbrakk>\<^sub>S = readS (TLBEntry56 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry56[liftState_simp]:
"\<lbrakk>write_reg TLBEntry56_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry56_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry55[liftState_simp]:
"\<lbrakk>read_reg TLBEntry55_ref\<rbrakk>\<^sub>S = readS (TLBEntry55 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry55[liftState_simp]:
"\<lbrakk>write_reg TLBEntry55_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry55_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry54[liftState_simp]:
"\<lbrakk>read_reg TLBEntry54_ref\<rbrakk>\<^sub>S = readS (TLBEntry54 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry54[liftState_simp]:
"\<lbrakk>write_reg TLBEntry54_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry54_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry53[liftState_simp]:
"\<lbrakk>read_reg TLBEntry53_ref\<rbrakk>\<^sub>S = readS (TLBEntry53 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry53[liftState_simp]:
"\<lbrakk>write_reg TLBEntry53_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry53_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry52[liftState_simp]:
"\<lbrakk>read_reg TLBEntry52_ref\<rbrakk>\<^sub>S = readS (TLBEntry52 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry52[liftState_simp]:
"\<lbrakk>write_reg TLBEntry52_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry52_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry51[liftState_simp]:
"\<lbrakk>read_reg TLBEntry51_ref\<rbrakk>\<^sub>S = readS (TLBEntry51 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry51[liftState_simp]:
"\<lbrakk>write_reg TLBEntry51_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry51_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry50[liftState_simp]:
"\<lbrakk>read_reg TLBEntry50_ref\<rbrakk>\<^sub>S = readS (TLBEntry50 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry50[liftState_simp]:
"\<lbrakk>write_reg TLBEntry50_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry50_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry49[liftState_simp]:
"\<lbrakk>read_reg TLBEntry49_ref\<rbrakk>\<^sub>S = readS (TLBEntry49 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry49[liftState_simp]:
"\<lbrakk>write_reg TLBEntry49_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry49_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry48[liftState_simp]:
"\<lbrakk>read_reg TLBEntry48_ref\<rbrakk>\<^sub>S = readS (TLBEntry48 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry48[liftState_simp]:
"\<lbrakk>write_reg TLBEntry48_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry48_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry47[liftState_simp]:
"\<lbrakk>read_reg TLBEntry47_ref\<rbrakk>\<^sub>S = readS (TLBEntry47 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry47[liftState_simp]:
"\<lbrakk>write_reg TLBEntry47_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry47_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry46[liftState_simp]:
"\<lbrakk>read_reg TLBEntry46_ref\<rbrakk>\<^sub>S = readS (TLBEntry46 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry46[liftState_simp]:
"\<lbrakk>write_reg TLBEntry46_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry46_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry45[liftState_simp]:
"\<lbrakk>read_reg TLBEntry45_ref\<rbrakk>\<^sub>S = readS (TLBEntry45 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry45[liftState_simp]:
"\<lbrakk>write_reg TLBEntry45_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry45_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry44[liftState_simp]:
"\<lbrakk>read_reg TLBEntry44_ref\<rbrakk>\<^sub>S = readS (TLBEntry44 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry44[liftState_simp]:
"\<lbrakk>write_reg TLBEntry44_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry44_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry43[liftState_simp]:
"\<lbrakk>read_reg TLBEntry43_ref\<rbrakk>\<^sub>S = readS (TLBEntry43 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry43[liftState_simp]:
"\<lbrakk>write_reg TLBEntry43_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry43_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry42[liftState_simp]:
"\<lbrakk>read_reg TLBEntry42_ref\<rbrakk>\<^sub>S = readS (TLBEntry42 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry42[liftState_simp]:
"\<lbrakk>write_reg TLBEntry42_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry42_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry41[liftState_simp]:
"\<lbrakk>read_reg TLBEntry41_ref\<rbrakk>\<^sub>S = readS (TLBEntry41 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry41[liftState_simp]:
"\<lbrakk>write_reg TLBEntry41_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry41_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry40[liftState_simp]:
"\<lbrakk>read_reg TLBEntry40_ref\<rbrakk>\<^sub>S = readS (TLBEntry40 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry40[liftState_simp]:
"\<lbrakk>write_reg TLBEntry40_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry40_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry39[liftState_simp]:
"\<lbrakk>read_reg TLBEntry39_ref\<rbrakk>\<^sub>S = readS (TLBEntry39 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry39[liftState_simp]:
"\<lbrakk>write_reg TLBEntry39_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry39_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry38[liftState_simp]:
"\<lbrakk>read_reg TLBEntry38_ref\<rbrakk>\<^sub>S = readS (TLBEntry38 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry38[liftState_simp]:
"\<lbrakk>write_reg TLBEntry38_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry38_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry37[liftState_simp]:
"\<lbrakk>read_reg TLBEntry37_ref\<rbrakk>\<^sub>S = readS (TLBEntry37 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry37[liftState_simp]:
"\<lbrakk>write_reg TLBEntry37_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry37_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry36[liftState_simp]:
"\<lbrakk>read_reg TLBEntry36_ref\<rbrakk>\<^sub>S = readS (TLBEntry36 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry36[liftState_simp]:
"\<lbrakk>write_reg TLBEntry36_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry36_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry35[liftState_simp]:
"\<lbrakk>read_reg TLBEntry35_ref\<rbrakk>\<^sub>S = readS (TLBEntry35 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry35[liftState_simp]:
"\<lbrakk>write_reg TLBEntry35_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry35_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry34[liftState_simp]:
"\<lbrakk>read_reg TLBEntry34_ref\<rbrakk>\<^sub>S = readS (TLBEntry34 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry34[liftState_simp]:
"\<lbrakk>write_reg TLBEntry34_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry34_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry33[liftState_simp]:
"\<lbrakk>read_reg TLBEntry33_ref\<rbrakk>\<^sub>S = readS (TLBEntry33 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry33[liftState_simp]:
"\<lbrakk>write_reg TLBEntry33_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry33_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry32[liftState_simp]:
"\<lbrakk>read_reg TLBEntry32_ref\<rbrakk>\<^sub>S = readS (TLBEntry32 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry32[liftState_simp]:
"\<lbrakk>write_reg TLBEntry32_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry32_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry31[liftState_simp]:
"\<lbrakk>read_reg TLBEntry31_ref\<rbrakk>\<^sub>S = readS (TLBEntry31 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry31[liftState_simp]:
"\<lbrakk>write_reg TLBEntry31_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry31_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry30[liftState_simp]:
"\<lbrakk>read_reg TLBEntry30_ref\<rbrakk>\<^sub>S = readS (TLBEntry30 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry30[liftState_simp]:
"\<lbrakk>write_reg TLBEntry30_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry30_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry29[liftState_simp]:
"\<lbrakk>read_reg TLBEntry29_ref\<rbrakk>\<^sub>S = readS (TLBEntry29 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry29[liftState_simp]:
"\<lbrakk>write_reg TLBEntry29_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry29_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry28[liftState_simp]:
"\<lbrakk>read_reg TLBEntry28_ref\<rbrakk>\<^sub>S = readS (TLBEntry28 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry28[liftState_simp]:
"\<lbrakk>write_reg TLBEntry28_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry28_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry27[liftState_simp]:
"\<lbrakk>read_reg TLBEntry27_ref\<rbrakk>\<^sub>S = readS (TLBEntry27 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry27[liftState_simp]:
"\<lbrakk>write_reg TLBEntry27_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry27_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry26[liftState_simp]:
"\<lbrakk>read_reg TLBEntry26_ref\<rbrakk>\<^sub>S = readS (TLBEntry26 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry26[liftState_simp]:
"\<lbrakk>write_reg TLBEntry26_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry26_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry25[liftState_simp]:
"\<lbrakk>read_reg TLBEntry25_ref\<rbrakk>\<^sub>S = readS (TLBEntry25 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry25[liftState_simp]:
"\<lbrakk>write_reg TLBEntry25_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry25_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry24[liftState_simp]:
"\<lbrakk>read_reg TLBEntry24_ref\<rbrakk>\<^sub>S = readS (TLBEntry24 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry24[liftState_simp]:
"\<lbrakk>write_reg TLBEntry24_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry24_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry23[liftState_simp]:
"\<lbrakk>read_reg TLBEntry23_ref\<rbrakk>\<^sub>S = readS (TLBEntry23 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry23[liftState_simp]:
"\<lbrakk>write_reg TLBEntry23_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry23_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry22[liftState_simp]:
"\<lbrakk>read_reg TLBEntry22_ref\<rbrakk>\<^sub>S = readS (TLBEntry22 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)
lemma liftS_write_reg_TLBEntry22[liftState_simp]:
"\<lbrakk>write_reg TLBEntry22_ref v\<rbrakk>\<^sub>S = updateS (regstate_update (TLBEntry22_update (\<lambda>_. v)))"
by (auto simp: liftState_write_reg_updateS register_defs)
lemma liftS_read_reg_TLBEntry21[liftState_simp]:
"\<lbrakk>read_reg TLBEntry21_ref\<rbrakk>\<^sub>S = readS (TLBEntry21 \<circ> regstate)"
by (auto simp: liftState_read_reg_readS register_defs)