2. k : Knd
3. l : IdLnk
4. ds : x:Id fp-> Type
5. da : a:Knd fp-> Type
6. f : (tg:Id
State(ds)
ma-valtype(da; k)(da(rcv(l; tg))?Void List)) List
7. source(l) = i
8. D' : Dsys
9. d-single-sends(i; ds; da; k; l; f)
D'
10. w : World
11. p : FairFifo
12. PossibleWorld(D';w)
13.
x:Id. vartype(i;x) r ds(x)?Top
14.
e:E. loc(e) = i 
(valtype(e) r ma-valtype(da; kind(e)))
15.
e:E. isrcv(e) lnk(e) = l (valtype(e) r ma-valtype(da; kind(e)))
16. {m:Msg| source(mlnk(m)) = i }
r Msg((
l,tg. da(rcv(l; tg))?Top))
17.
e:E.
17. loc(e) = i
17.
17. kind(e) = k
sends(l;e) = tagged-messages(l;z.(z when e);val(e);f)
18.
x:Id. vartype(i;x) r ds(x)?Top
19.
e:E. loc(e) = i (valtype(e) r ma-valtype(da; kind(e)))
20.
e:E. isrcv(e) lnk(e) = l (valtype(e) r ma-valtype(da; kind(e)))
21. e : E
22. loc(e) = i
23. kind(e) = k
24. valtype(e)
r ma-valtype(da; kind(e))
25. sends(l;e) = tagged-messages(l;
z.(z when e);val(e);f)
26. valtype(e)
r ma-valtype(da; kind(e))
27. L :
27.
n:
||sends(l;e)||.
27.
e':E. isrcv(e') & lnk(e') = l & sender(e') = e & index(e') = n
28. LL :
28. n:
||sends(l;e)||{e':E
28. n:
||sends(l;e)||{| isrcv(e')
28. n:
||sends(l;e)||{| & lnk(e') = l & sender(e') = e & index(e') = n }
29. (
n.1of(L(n))) = LL
30.
e:E.
30. isrcv(e)
sends(lnk(e);sender(e))[index(e)] = msg(lnk(e);tag(e);val(e))
31.
e:E, l:IdLnk, n:||sends(l;e)||.
31.
e':E. isrcv(e') & lnk(e') = l & sender(e') = e & index(e') = n
32. (Msg on l)
r (IdLnk(tg:Idma-valtype(da; rcv(l; tg))))
33. map(LL;upto(||sends(l;e)||))
33.
{e':E| isrcv(e') & lnk(e') = l & sender(e') = e } List
34. ||upto(||sends(l;e)||)|| = ||sends(l;e)||
35. ||map(LL;upto(||sends(l;e)||))|| = ||sends(l;e)||
36. ||map(
e'.<tag(e'),val(e')>;map(LL;upto(||sends(l;e)||)))|| = ||sends(l;e)||
37. i1 :
38. i1<||map(
e'.<tag(e'),val(e')>;map(LL;upto(||sends(l;e)||)))||
39. v : E
40. isrcv(v)
41. lnk(v) = l
42. sender(v) = e
43. index(v) = i1
<tag(v),val(v)> = 2of(sends(l;e)[i1]) tg:Idma-valtype(da; rcv(l; tg))
