At: switch inv rel closure lemma1 1 1 2 1 1 2 1 2 1 2
1. E: EventStruct
2. tr: |E| List
3. ls: 
||tr||
4. is-send(E)(tr[ls])
5. 
j:||tr||. ls < j 
is-send(E)(tr[j])
6. n: 
7. 0 < n
8. i,j:||tr||.
i
j is-send(E)(tr[i]) is-send(E)(tr[j]) (i switchR(tr)^n-1 ls) (j (switchR(tr)^*) ls)
9. i: ||tr||
10. j: ||tr||
11. ij
12. is-send(E)(tr[i])
13. is-send(E)(tr[j])
14. i switchR(tr)^n ls
15. n = 0
16. z: ||tr||
17. is-send(E)(tr[i])
18. is-send(E)(tr[z])
19. i < z
20. tr[z] somewhere delivered before tr[i]
21. z switchR(tr)^n-1 ls
22. i (switchR(tr)^*) ls
23. z (switchR(tr)^*) ls
24. zj
25. j = i
26. tr[z] somewhere delivered before tr[j]
27. j switchR(tr) z
j (switchR(tr)^*) ls
By: BackThruLemma'
Thm* R:(T
TProp), x,y,z:T. (x R y) (y (R^*) z) (x (R^*) z)
Generated subgoals:None
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