Thm* M1,M2:MsgA.
Thm* M1 M2
Thm* 
Thm* ( k:Knd, l:IdLnk, s:M2.state, v:M2.da(k), i:Id, ms:(tg:Id
Thm* ( k:Knd, l:IdLnk, s:M2.state, v:M2.da(k), i:Id, ms:( if source(l) = i
Thm* ( k:Knd, l:IdLnk, s:M2.state, v:M2.da(k), i:Id, ms:( if M2.da(rcv(l; tg))
Thm* ( k:Knd, l:IdLnk, s:M2.state, v:M2.da(k), i:Id, ms:( else Top fi) List.
Thm* (M2.send(k;l;s;v;ms;i)  M1.send(k;l;s;v;ms;i)) | [ma-send-sub] |
Thm* M:MsgA, k:Knd, l:IdLnk, s:M.state, v:M.V(k), i:Id, ms:(tg:Id
Thm* M:MsgA, k:Knd, l:IdLnk, s:M.state, v:M.V(k), i:Id, ms:( if source(l) = i
Thm* M:MsgA, k:Knd, l:IdLnk, s:M.state, v:M.V(k), i:Id, ms:( if M.da(rcv
Thm* M:MsgA, k:Knd, l:IdLnk, s:M.state, v:M.V(k), i:Id, ms:( if (l; tg))
Thm* M:MsgA, k:Knd, l:IdLnk, s:M.state, v:M.V(k), i:Id, ms:( else Top fi) List.
Thm* M.send(k;l;s;v;ms;i) Prop | [ma-send_wf] |
Thm* eq:EqDecider(A), f,g:a:A fp-> Top, x:A, z:Top.
Thm* f g(x)?z ~ if x dom(f) f(x)?z else g(x)?z fi | [fpf-join-cap-sq] |
Thm* B:(A Type), eq:EqDecider(A), f,g:a:A fp-> B(a), x:A.
Thm* x dom(f g)  f g(x) = if x dom(f) f(x) else g(x) fi B(x) | [fpf-join-ap] |
Def @i (with ds: ds init: init action a:T precondition a(v) is P s v)(j)
Def == if eqof(IdDeq)(j,i)
Def == if (with ds: ds
Def == if (init: init
Def == if action a:T
Def == if aprecondition a(v) is
Def == if aP)
Def == else fi | [d-single-pre-init] |
Def @i (with ds: ds action a:T precondition a(v) is P s v)(j)
Def == if eqof(IdDeq)(j,i) (with ds: ds action a:T precondition a(v) is P s v)
Def == else fi | [d-single-pre] |
Def d-single-sends(i; ds; da; k; l; f)(j)
Def == if eqof(IdDeq)(j,i) ma-single-sends(ds; da; k; l; f) else fi | [d-single-sends] |
Def d-single-effect(i; ds; da; k; x; f)(j)
Def == if eqof(IdDeq)(j,i) ma-single-effect(ds; da; k; x; f) else fi | [d-single-effect] |
Def @i: only L sends on (l with tg)(j)
Def == if eqof(IdDeq)(j,i) only L sends on (l with tg) else fi | [d-single-sframe] |
Def @i: only L affects x : t(j)
Def == if eqof(IdDeq)(j,i) only members of L affect x :t else fi | [d-single-frame] |
Def @i: x:T initially x = v(j)
Def == if eqof(IdDeq)(j,i) x : T initially x = v else fi | [d-single-init] |