1 | 1. E: EventStruct 2. P: (Label (|E| List)) Prop 3. f,g:(Label (|E| List)). ( p:Label. g(p) f(p))  P(f)  P(g) 4. f,g:(Label (|E| List)).
( a:|E|. p:Label. g(p) = filter( b. (b =msg=(E) a);f(p)))  P(f)  P(g) 5. 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) safetyR(E) preserves tr.P( p.tr delivered at p) |
2 | 1. E: EventStruct 2. P: (Label (|E| List)) Prop 3. f,g:(Label (|E| List)). ( p:Label. g(p) f(p))  P(f)  P(g) 4. f,g:(Label (|E| List)).
( a:|E|. p:Label. g(p) = filter( b. (b =msg=(E) a);f(p)))  P(f)  P(g) 5. 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) memorylessR(E) preserves tr.P( p.tr delivered at p) |
3 | 1. E: EventStruct 2. P: (Label (|E| List)) Prop 3. f,g:(Label (|E| List)). ( p:Label. g(p) f(p))  P(f)  P(g) 4. f,g:(Label (|E| List)).
( a:|E|. p:Label. g(p) = filter( b. (b =msg=(E) a);f(p)))  P(f)  P(g) 5. 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) (ternary) composableR(E) preserves tr.P( p.tr delivered at p) |
4 | 1. E: EventStruct 2. P: (Label (|E| List)) Prop 3. f,g:(Label (|E| List)). ( p:Label. g(p) f(p))  P(f)  P(g) 4. f,g:(Label (|E| List)).
( a:|E|. p:Label. g(p) = filter( b. (b =msg=(E) a);f(p)))  P(f)  P(g) 5. 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) send-enabledR(E) preserves tr.P( p.tr delivered at p) |
5 | 1. E: EventStruct 2. P: (Label (|E| List)) Prop 3. f,g:(Label (|E| List)). ( p:Label. g(p) f(p))  P(f)  P(g) 4. f,g:(Label (|E| List)).
( a:|E|. p:Label. g(p) = filter( b. (b =msg=(E) a);f(p)))  P(f)  P(g) 5. 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) asyncR(E) preserves tr.P( p.tr delivered at p) |
6 | 1. E: EventStruct 2. P: (Label (|E| List)) Prop 3. f,g:(Label (|E| List)). ( p:Label. g(p) f(p))  P(f)  P(g) 4. f,g:(Label (|E| List)).
( a:|E|. p:Label. g(p) = filter( b. (b =msg=(E) a);f(p)))  P(f)  P(g) 5. 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) delayableR(E) preserves tr.P( p.tr delivered at p) |