Thm* E:EventStruct, P:((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. ( x f(p).( y g(q). (x =msg=(E) y)))) 
( p:Label. h(p) = ((f(p)) @ (g(p))))  P(f)  P(g)  P(h))

switchable0(E)(local_deliver_property(E;P)) | [local_deliver_switchable] |
Def send-enabledR(E)(L_1,L_2) == x:|E|. (is-send(E)(x)) & L_2 = (L_1 @ [x]) | [R_send_enabled] |
Def composableR(E)(L_1,L_2,L)
== ( x L_1.( y L_2. (x =msg=(E) y))) & L = (L_1 @ L_2) |E| List | [R_composable] |
Def single-tag-decomposable(E)(L)
== L = nil |E| List 
( L_1,L_2:Trace(E).
L = (L_1 @ L_2) |E| List
& L_2 = nil |E| List
& ( x L_1.( y L_2. (x =msg=(E) y)))
& ( m:Label. ( x L_2.tag(E)(x) = m))) | [single_tag_decomposable] |