(Label(|E| List))Prop

f,g:(Label(|E| List)). (p:Label. g(p) f(p)) P(f) P(g)

f,g:(Label(|E| List)). (a:|E|. p:Label. g(p) = filter(b.(b =msg=(E) a);f(p))) P(f) P(g)

f,g,h:(Label(|E| List)). (p,q:Label. (xf(p).(yg(q).(x =msg=(E) y)))) (p:Label. h(p) = ((f(p)) @ (g(p)))) P(f) P(g) P(h)

P(p.x delivered at p)

x swap adjacent[loc(E)(x) = loc(E)(y) & is-send(E)(x) & is-send(E)(y) is-send(E)(x) & is-send(E)(y)] y

(||filter(e.is-send(E)(e)loc(E)(e) = x1;x)||-1)

is-send(E)(filter(e.is-send(E)(e)loc(E)(e) = x1;x)[i]) & is-send(E)(filter(e.is-send(E)(e)loc(E)(e) = x1;x)[(i+1)]) is-send(E)(filter(e.is-send(E)(e)loc(E)(e) = x1;x)[i]) & is-send(E)(filter(e.is-send(E)(e)loc(E)(e) = x1;x)[(i+1)])

filter(e.is-send(E)(e)loc(E)(e) = x1;y) = swap(filter(e.is-send(E)(e)loc(E)(e) = x1;x);i;i+1)

x@0:|E|. (x@0 filter(e.is-send(E)(e)loc(E)(e) = x1;x)) is-send(E)(x@0) & loc(E)(x@0) = x1

loc(E)(filter(e.is-send(E)(e)loc(E)(e) = x1;x)[i]) = x1

x1 = loc(E)(filter(e.is-send(E)(e)loc(E)(e) = x1;x)[(i+1)])

1	loc(E)(filter(e.is-send(E)(e)loc(E)(e) = x1;x)[(i+1)]) = x1

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