Nuprl - Proof: world-event-system 13 2 2 2 1 2 1 2 2 1 1

(248steps total) PrintForm Definitions Lemmas mb event system 3 Sections EventSystems Doc

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At: world-event-system 13 2 2 2 1 2 1 2 2 1 1

1. the_w : World
2. FairFifo
3.

e,e':E. loc(e) = loc(e')

e <c e'

e = e'

e' <c e
4.

e:E. first(e)

(

e':E. loc(e') = loc(e)

e' <c e)
5.

e:E.
5.

first(e)
5.

5. loc(pred(e)) = loc(e) & pred(e) <c e
5. & (

e':E. loc(e') = loc(e)

(pred(e) <c e' & e' <c e))
6.

e:E.

first(e)

(

x:Id. (x when e) = (x after pred(e)))
7. Trans e,e':E. e <c e'
8. SWellFounded(e <c e')
9.

e:E.
9. isrcv(kind(e))
9.

9. sends(lnk(kind(e));sender(e))[index(e)]
9. =
9. msg(lnk(kind(e));tag(kind(e));val(e))
10.

e:E. isrcv(kind(e))

sender(e) <c e
11.

e,e':E.
11. e <c e'
11.

11.

first(e') & e <c pred(e')

e = pred(e')
11.

isrcv(kind(e')) & e <c sender(e')

e = sender(e')
12.

e:E. isrcv(kind(e))

loc(e) = destination(lnk(kind(e)))
13.

e:E, l:IdLnk.

loc(e) = source(l)

sends(l;e) = nil
14.

e,e':E.
14. isrcv(kind(e))
14.

14. isrcv(kind(e'))
14.

14. lnk(kind(e)) = lnk(kind(e'))
14.

14. (e <c e'
14. (

14. (sender(e) <c sender(e')

sender(e) = sender(e') & index(e)<index(e'))
15.

, l:IdLnk, t:

. m

||snds(l;t)||

(

t':

. t

t' & m

||rcvs(l;t')||)
16. e : E
17. l : IdLnk
18. n :

||sends(l;e)||
19. t' :

20. time(e)+1

t'
21. t :

22. <destination(l),t>

E
23.

isnull(a(destination(l);t))
24. isrcv(kind(a(destination(l);t)))
25. ||snds(l;time(e))||+n+1

||rcvs(l;t')||
26. lnk(kind(a(destination(l);t))) = l
27. ||rcvs(l;t)|| = ||snds(l;time(e))||+n
28. True
29. lnk(kind(a(destination(l);t))) = l
30. isrcv(kind(<destination(l),t>))

(source(lnk(kind(a(destination(l);t)))) = 1of(e)

((mu(

t@0.match(lnk(kind(a(destination(l);t)));t@0;t))=

2of(e)))

& ||rcvs(lnk(kind(a(destination(l);t)));t)||

& -||snds(lnk(kind(a(destination(l);t)));mu(

t@0.

& match(lnk(kind(a(destination(l);t)));t@0;t)))||

& =

& n

By:	Assert match(l;time(e);t)

Generated subgoals:

1   match(l;time(e);t)
6 steps

2 31. match(l;time(e);t)
  (source(lnk(kind(a(destination(l);t)))) = 1of(e)
  ((mu(t@0.match(lnk(kind(a(destination(l);t)));t@0;t))=2of(e)))
  & ||rcvs(lnk(kind(a(destination(l);t)));t)||
  & -||snds(lnk(kind(a(destination(l);t)));mu(t@0.
  & match(lnk(kind(a(destination(l);t)));t@0;t)))||
  & =
  & n
8 steps

About:

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(248steps total) PrintForm Definitions Lemmas mb event system 3 Sections EventSystems Doc

1	match(l;time(e);t)	6 steps
2	31. match(l;time(e);t) (source(lnk(kind(a(destination(l);t)))) = 1of(e) ((mu(t@0.match(lnk(kind(a(destination(l);t)));t@0;t))=2of(e))) & \|\|rcvs(lnk(kind(a(destination(l);t)));t)\|\| & -\|\|snds(lnk(kind(a(destination(l);t)));mu(t@0. & match(lnk(kind(a(destination(l);t)));t@0;t)))\|\| & = & n	8 steps