Nuprl - Pf strong_switch_inv_decomposable 1 2 1 1 2 2 1 2 1

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At: strong switch inv decomposable 1 2 1 1 2 2 1 2 1

1. E: TaggedEventStruct
2. tr: |E| List
3. Causal(E)(tr)
4. AD-normal(E)(tr)
5. No-dup-deliver(E)(tr)
6. tr = nil
7. ls: ||tr||
8. is-send(E)(tr[ls])
9. j:||tr||. ls < j is-send(E)(tr[j])
10. i:||tr||. (i (switchR(tr)^*) ls) is-send(E)(tr[i])
11. EquivRel(|E|)(_1 =msg=(E) _2)
12. i,j:||tr||. ij is-send(E)(tr[j]) (i (switchR(tr)^*) ls) (j (switchR(tr)^*) ls)
13. d:
14. 0 < d
15. i,j:||tr||. d-1 = j-i (i (switchR(tr)^*) ls) ij (k:||tr||. (k (switchR(tr)^*) ls) & (tr[k] =msg=(E) tr[j]))
16. i: ||tr||
17. j: ||tr||
18. d = j-i
19. i (switchR(tr)^*) ls
20. ij
21. is-send(E)(tr[i])
22. is-send(E)(tr[j])
23. ij-1
24. is-send(E)(tr[(j-1)])
25. k: ||tr||
26. k (switchR(tr)^*) ls
27. tr[k] =msg=(E) tr[(j-1)]

k:||tr||. (k (switchR(tr)^*) ls) & (tr[k] =msg=(E) tr[j])

By: AllHyps (h.(Unfold `P_causal` h) THEN (Reduce h) THEN (InstHyp [j] h)) THEN ExRepD

Generated subgoal:

1 3. i:||tr||. j:||tr||. ji & is-send(E)(tr[j]) & (tr[j] =msg=(E) tr[i])
4. AD-normal(E)(tr)
5. No-dup-deliver(E)(tr)
6. tr = nil
7. ls: ||tr||
8. is-send(E)(tr[ls])
9. j:||tr||. ls < j is-send(E)(tr[j])
10. i:||tr||. (i (switchR(tr)^*) ls) is-send(E)(tr[i])
11. EquivRel(|E|)(_1 =msg=(E) _2)
12. i,j:||tr||. ij is-send(E)(tr[j]) (i (switchR(tr)^*) ls) (j (switchR(tr)^*) ls)
13. d:
14. 0 < d
15. i,j:||tr||. d-1 = j-i (i (switchR(tr)^*) ls) ij (k:||tr||. (k (switchR(tr)^*) ls) & (tr[k] =msg=(E) tr[j]))
16. i: ||tr||
17. j: ||tr||
18. d = j-i
19. i (switchR(tr)^*) ls
20. ij
21. is-send(E)(tr[i])
22. is-send(E)(tr[j])
23. ij-1
24. is-send(E)(tr[(j-1)])
25. k: ||tr||
26. k (switchR(tr)^*) ls
27. tr[k] =msg=(E) tr[(j-1)]
28. j@0: ||tr||
29. j@0j
30. is-send(E)(tr[j@0])
31. tr[j@0] =msg=(E) tr[j]
k:||tr||. (k (switchR(tr)^*) ls) & (tr[k] =msg=(E) tr[j])

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