Nuprl - mb_event_system_7 Citations of and

mb event system 7 Sections EventSystems Doc

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Def P & Q == P

is mentioned by

Thm* R:(Id), uid:(|R|), out,in:(|R|IdLnk).
Thm* ring(R;in;out)
Thm*
Thm* Inj(|R|; ; uid)
Thm*
Thm* loc.(ring-leader1(loc;R;uid;out;in))
Thm* realizes es.ldr:|R|.
Thm* realizes es.e@ldr.kind(e) = locl("leader")
Thm* realizes es.& (i:|R|. e@i.kind(e) = locl("leader")  i = ldr  |R|) [ring-leader1__realizes]

Thm* R:(Id), in,out:(|R|IdLnk).
Thm* ring(R;in;out)  (L:|R| List. 0<||L|| & (i:|R|. (i  L))) [ring-list]

Thm* R:(Id), in,out:(|R|IdLnk), i,j:|R|.
Thm* ring(R;in;out)
Thm*
Thm* x.n(x)^d(i;j)(i) = j & (k:. k<d(i;j)  x.n(x)^k(i) = j) [rdist-property]

Thm* P:(AT), i:Id, k:Knd, a,x:Id.
Thm* A
Thm*
Thm* T
Thm*
Thm* x = "trigger"
Thm*
Thm* locl(a) = k
Thm*
Thm* loc.(trigger1(loc;T;A;P;i;k;a;x))
Thm* realizes es.(vartype(i;x) r A)
Thm* realizes es.& e@i.kind(e) = k  Knd  (valtype(e) r T)
Thm* realizes es.& e'@i.kind(e') = locl(a)
Thm* realizes es.& e'@i.
Thm* realizes es.& (e:E.
Thm* realizes es.& ((e <loc e') & kind(e) = k  Knd & P((x when e),val(e)))
Thm* realizes es.& e@i.kind(e) = k  Knd
Thm* realizes es.& e@i.
Thm* realizes es.& P((x when e),val(e))  e'@i.kind(e') = locl(a)  Knd [trigger1__realizes]

Thm* P:(AT), k:Knd, i,r,x:Id.
Thm* A
Thm*
Thm* T
Thm*
Thm* x = r
Thm*
Thm* loc.(recognizer1(loc;T;A;P;k;i;r;x))
Thm* realizes es.e@i.kind(e) = k  Knd  (valtype(e) r T)
Thm* realizes es.& (vartype(i;x) r A)
Thm* realizes es.& e@i.first(e)  (r when e) = false
Thm* realizes es.& e'@i.(r after e')
Thm* realizes es.& e'@i.
Thm* realizes es.& e'@i.(e:E.
Thm* realizes es.& e'@i.((e <loc e')  e = e'  E
Thm* realizes es.& e'@i.(& kind(e) = k  Knd
Thm* realizes es.& e'@i.(& P((x when e),val(e))) [recognizer1__realizes]

Thm* a:Id, f:(AT), tg:Id, l:IdLnk, x:Id.
Thm* "done" = x
Thm*
Thm* A
Thm*
Thm* T
Thm*
Thm* loc.(send-once(loc;T;A;a;f;tg;l;x))
Thm* realizes es.(vartype(source(l);x) r A)
Thm* realizes es.& (e:E. kind(e) = rcv(l; tg)  Knd  (valtype(e) r T))
Thm* realizes es.& (e:E.
Thm* realizes es.& (kind(e) = rcv(l; tg)  Knd
Thm* realizes es.& (& val(e) = f((x when sender(e)))  T
Thm* realizes es.& (& & kind(sender(e)) = locl(a)  Knd
Thm* realizes es.& (& & (e':E.
Thm* realizes es.& (& & (kind(e') = rcv(l; tg)  Knd
Thm* realizes es.& (& & (
Thm* realizes es.& (& & (kind(sender(e')) = locl(a)  Knd  e' = e  E)) [send-once__realizes]

Thm* a,i:Id.
Thm* loc.(once(loc;a;i))
Thm* realizes es.e@i.kind(e) = locl(a)
Thm* realizes es.& e@i.e'@i.kind(e) = locl(a)
Thm* realizes es.& e@i.e'@i.
Thm* realizes es.& kind(e') = locl(a)  Knd  e = e'  E [once__realizes]

Thm* i,x:Id, k:Knd, T:Type.
Thm* @i: only members of [k] affect x :T  Dsys
Thm* & (D:Dsys.
Thm* & (@i: only members of [k] affect x :T  D
Thm* & (
Thm* & (D
Thm* & (realizes es.(vartype(i;x) r T)
Thm* & (realizes es.& e@i.((x after e) = (x when e)  T  kind(e) = k  Knd)
Thm* & (realizes es.& & (kind(e) = k  Knd  (x after e) = (x when e)  T)) [frame-rule1]

Thm* i,a,x:Id, A,T:Type, c:A, P:(ATProp).
Thm* @i: ma-single-pre-init1(x;A;c;a;T;x,v.P(x,v))  Dsys
Thm* & (D:Dsys.
Thm* & (@i: ma-single-pre-init1(x;A;c;a;T;x,v.P(x,v))  D
Thm* & (
Thm* & (D
Thm* & (realizes es.(vartype(i;x) r A)
Thm* & (realizes es.& (e:E. loc(e) = i  Id  first(e)  (x when e) = c  A)
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = i  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = locl(a)  Knd  (valtype(e) r T))
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = i  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = locl(a)  Knd  P((x when e),val(e)))
Thm* & (realizes es.& & ((v:T. P(c,v))
Thm* & (realizes es.& & (
Thm* & (realizes es.& & ((e:E.
Thm* & (realizes es.& & ((loc(e) = i  Id
Thm* & (realizes es.& & ((& kind(e) = locl(a)  Knd
Thm* & (realizes es.& & ((&  (v:T. P((x after e),v))))) [s-pre-init-rule1]

Thm* i:Id, L:Knd List, x:Id, T:Type.
Thm* @i: only members of L affect x :T  Dsys
Thm* & (D:Dsys.
Thm* & (@i: only members of L affect x :T  D
Thm* & (
Thm* & (D
Thm* & (realizes es.(vartype(i;x) r T)
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = i  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (((x after e) = (x when e)  T  (kind(e)  L))
Thm* & (realizes es.& (& ((kind(e)  L)  (x after e) = (x when e)  T))) [s-frame-rule]

Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type.
Thm* (rcv(l; tg) = k  T = B)
Thm*
Thm* (f:(ABT), c:(AB).
Thm* (@source(l): ma-single-sends1(A;
Thm* (@source(l): ma-single-sends1(B;
Thm* (@source(l): ma-single-sends1(T;
Thm* (@source(l): ma-single-sends1(x;
Thm* (@source(l): ma-single-sends1(k;
Thm* (@source(l): ma-single-sends1(l;
Thm* (@source(l): ma-single-sends1(tg;
Thm* (@source(l): ma-single-sends1((a,b. if c(a,b) [(f(a,b))] else nil fi))
Thm* ( Dsys
Thm* (& (D:Dsys.
Thm* (& (@source(l): ma-single-sends1(A;
Thm* (& (@source(l): ma-single-sends1(B;
Thm* (& (@source(l): ma-single-sends1(T;
Thm* (& (@source(l): ma-single-sends1(x;
Thm* (& (@source(l): ma-single-sends1(k;
Thm* (& (@source(l): ma-single-sends1(l;
Thm* (& (@source(l): ma-single-sends1(tg;
Thm* (& (@source(l): ma-single-sends1((a,b. if c(a,b) [(f(a,b))] else nil fi)
Thm* (& (@source(l): ma-single-sends1()  D
Thm* (& (
Thm* (& (D
Thm* (& (realizes es.(vartype(source(l);x) r A)
Thm* (& (realizes es.& (e:E.
Thm* (& (realizes es.& (loc(e) = source(l)  Id
Thm* (& (realizes es.& (
Thm* (& (realizes es.& (kind(e) = k  Knd  (valtype(e) r B))
Thm* (& (realizes es.& (e:E. kind(e) = rcv(l; tg)  Knd  (valtype(e) r T))
Thm* (& (realizes es.& (e:E.
Thm* (& (realizes es.& (loc(e) = source(l)  Id
Thm* (& (realizes es.& (
Thm* (& (realizes es.& (kind(e) = k  Knd
Thm* (& (realizes es.& (
Thm* (& (realizes es.& ((c((x when e),val(e))
Thm* (& (realizes es.& ((
Thm* (& (realizes es.& (((e':E.
Thm* (& (realizes es.& (((kind(e') = rcv(l; tg)  Knd
Thm* (& (realizes es.& (((& sender(e') = e  E
Thm* (& (realizes es.& (((& & (e'':E.
Thm* (& (realizes es.& (((& & (kind(e'') = rcv(l; tg)  Knd
Thm* (& (realizes es.& (((& & (
Thm* (& (realizes es.& (((& & (sender(e'') = e  E  e'' = e'  E)
Thm* (& (realizes es.& (((& & val(e') = f((x when e),val(e))  T))
Thm* (& (realizes es.& (& (c((x when e),val(e))
Thm* (& (realizes es.& (& (
Thm* (& (realizes es.& (& ((e':E.
Thm* (& (realizes es.& (& ((kind(e') = rcv(l; tg)  Knd
Thm* (& (realizes es.& (& ((& sender(e') = e  E))))) [conditional-send1-rule]

Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type.
Thm* (rcv(l; tg) = k  T = B)
Thm*
Thm* (f:(ABT).
Thm* (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; (a,b. [(f(a,b))]))
Thm* ( Dsys
Thm* (& (D:Dsys.
Thm* (& (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; (a,b. [(f(a,b))])
Thm* (& (@source(l): ma-single-sends1()  D
Thm* (& (
Thm* (& (D
Thm* (& (realizes es.(vartype(source(l);x) r A)
Thm* (& (realizes es.& (e:E.
Thm* (& (realizes es.& (loc(e) = source(l)  Id
Thm* (& (realizes es.& (
Thm* (& (realizes es.& (kind(e) = k  Knd  (valtype(e) r B))
Thm* (& (realizes es.& (e:E. kind(e) = rcv(l; tg)  Knd  (valtype(e) r T))
Thm* (& (realizes es.& (e:E.
Thm* (& (realizes es.& (loc(e) = source(l)  Id
Thm* (& (realizes es.& (
Thm* (& (realizes es.& (kind(e) = k  Knd
Thm* (& (realizes es.& (
Thm* (& (realizes es.& ((e':E.
Thm* (& (realizes es.& ((kind(e') = rcv(l; tg)  Knd
Thm* (& (realizes es.& ((& sender(e') = e  E
Thm* (& (realizes es.& ((& & (e'':E.
Thm* (& (realizes es.& ((& & (kind(e'') = rcv(l; tg)  Knd
Thm* (& (realizes es.& ((& & (
Thm* (& (realizes es.& ((& & (sender(e'') = e  E  e'' = e'  E)
Thm* (& (realizes es.& ((& & val(e') = f((x when e),val(e))  T)))) [s-unconditional-send1-rule]

Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type, f:(AB(T List)).
Thm* (rcv(l; tg) = k  T = B)
Thm*
Thm* @source(l): ma-single-sends1(A; B; T; x; k; l; tg; f)  Dsys
Thm* & (D:Dsys.
Thm* & (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; f)  D
Thm* & (
Thm* & (D
Thm* & (realizes es.(vartype(source(l);x) r A)
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = source(l)  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = k  Knd  (valtype(e) r B))
Thm* & (realizes es.& (e:E. kind(e) = rcv(l; tg)  Knd  (valtype(e) r T))
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = source(l)  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = k  Knd
Thm* & (realizes es.& (
Thm* & (realizes es.& ((L:{e':E| kind(e') = rcv(l; tg)  Knd } List.
Thm* & (realizes es.& (((e':E.
Thm* & (realizes es.& ((((e'  L)
Thm* & (realizes es.& (((
Thm* & (realizes es.& (((kind(e') = rcv(l; tg)  Knd & sender(e') = e  E)
Thm* & (realizes es.& ((& (e1,e2:E. e1 before e2  L  (e1 <loc e2))
Thm* & (realizes es.& ((& map(e'.val(e');L) = f((x when e),val(e))  T List))) [s-sends-rule1]

Def spanner(f;T;to;from)
Def == (l:Edge(T). f(l) = f(inverse(l)))
Def == & (i:|T|, l1,l2:Edge(T).
Def == & ((l1  to(i))
Def == & (
Def == & ((l2  to(i))  l1 = l2  IdLnk  (f(l1))  (f(l2))) [spanner]

Def bi-tree(T;to;from)
Def == bi-graph(T;to;from)
Def == & (i,j:|T|.
Def == & (p:Edge(T) List.
Def == & (lconnects(p;i;j) & (q:Edge(T) List. lconnects(q;i;j)  q = p))
Def == & (L:|T| List. i:|T|. (i  L))
Def == & |T| [bi-tree]

Def bi-graph(G;to;from)
Def == i:|G|.
Def == (lto(i).destination(l) = i
Def == & (G(source(l)))
Def == & (l  from(source(l)))
Def == & (lnk-inv(l)  from(i)))
Def == & (lfrom(i).source(l) = i
Def == & & (G(destination(l)))
Def == & & (l  to(destination(l)))
Def == & & (lnk-inv(l)  to(i))) [bi-graph]

Def ring(R;in;out)
Def == (i:|R|.
Def == ((R(source(in(i)))) & (R(destination(out(i))))
Def == (& source(out(i)) = i
Def == (& & destination(in(i)) = i
Def == (& & in(destination(out(i))) = out(i)  IdLnk
Def == (& & out(source(in(i))) = in(i)  IdLnk)
Def == & (i,j:|R|. k:. x.destination(out(x))^k(i) = j  Id)
Def == & |R| [ring]

In prior sections: core int 1 bool 1 int 2 mb nat mb list 1 num thy 1 mb list 2 mb event system 1 mb event system 2 mb event system 3 mb event system 5 mb event system 6 fun 1 rel 1 mb event system 4

Try larger context: EventSystems IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html

mb event system 7 Sections EventSystems Doc

Thm* R:(Id), uid:(\|R\|), out,in:(\|R\|IdLnk). Thm* ring(R;in;out) Thm* Thm* Inj(\|R\|; ; uid) Thm* Thm* loc.(ring-leader1(loc;R;uid;out;in)) Thm* realizes es.ldr:\|R\|. Thm* realizes es.e@ldr.kind(e) = locl("leader") Thm* realizes es.& (i:\|R\|. e@i.kind(e) = locl("leader") i = ldr \|R\|)	[ring-leader1__realizes]
Thm* R:(Id), in,out:(\|R\|IdLnk). Thm* ring(R;in;out) (L:\|R\| List. 0<\|\|L\|\| & (i:\|R\|. (i L)))	[ring-list]
Thm* R:(Id), in,out:(\|R\|IdLnk), i,j:\|R\|. Thm* ring(R;in;out) Thm* Thm* x.n(x)^d(i;j)(i) = j & (k:. k<d(i;j) x.n(x)^k(i) = j)	[rdist-property]
Thm* P:(AT), i:Id, k:Knd, a,x:Id. Thm* A Thm* Thm* T Thm* Thm* x = "trigger" Thm* Thm* locl(a) = k Thm* Thm* loc.(trigger1(loc;T;A;P;i;k;a;x)) Thm* realizes es.(vartype(i;x) r A) Thm* realizes es.& e@i.kind(e) = k Knd (valtype(e) r T) Thm* realizes es.& e'@i.kind(e') = locl(a) Thm* realizes es.& e'@i. Thm* realizes es.& (e:E. Thm* realizes es.& ((e <loc e') & kind(e) = k Knd & P((x when e),val(e))) Thm* realizes es.& e@i.kind(e) = k Knd Thm* realizes es.& e@i. Thm* realizes es.& P((x when e),val(e)) e'@i.kind(e') = locl(a) Knd	[trigger1__realizes]
Thm* P:(AT), k:Knd, i,r,x:Id. Thm* A Thm* Thm* T Thm* Thm* x = r Thm* Thm* loc.(recognizer1(loc;T;A;P;k;i;r;x)) Thm* realizes es.e@i.kind(e) = k Knd (valtype(e) r T) Thm* realizes es.& (vartype(i;x) r A) Thm* realizes es.& e@i.first(e) (r when e) = false Thm* realizes es.& e'@i.(r after e') Thm* realizes es.& e'@i. Thm* realizes es.& e'@i.(e:E. Thm* realizes es.& e'@i.((e <loc e') e = e' E Thm* realizes es.& e'@i.(& kind(e) = k Knd Thm* realizes es.& e'@i.(& P((x when e),val(e)))	[recognizer1__realizes]
Thm* a:Id, f:(AT), tg:Id, l:IdLnk, x:Id. Thm* "done" = x Thm* Thm* A Thm* Thm* T Thm* Thm* loc.(send-once(loc;T;A;a;f;tg;l;x)) Thm* realizes es.(vartype(source(l);x) r A) Thm* realizes es.& (e:E. kind(e) = rcv(l; tg) Knd (valtype(e) r T)) Thm* realizes es.& (e:E. Thm* realizes es.& (kind(e) = rcv(l; tg) Knd Thm* realizes es.& (& val(e) = f((x when sender(e))) T Thm* realizes es.& (& & kind(sender(e)) = locl(a) Knd Thm* realizes es.& (& & (e':E. Thm* realizes es.& (& & (kind(e') = rcv(l; tg) Knd Thm* realizes es.& (& & ( Thm* realizes es.& (& & (kind(sender(e')) = locl(a) Knd e' = e E))	[send-once__realizes]
Thm* a,i:Id. Thm* loc.(once(loc;a;i)) Thm* realizes es.e@i.kind(e) = locl(a) Thm* realizes es.& e@i.e'@i.kind(e) = locl(a) Thm* realizes es.& e@i.e'@i. Thm* realizes es.& kind(e') = locl(a) Knd e = e' E	[once__realizes]
Thm* i,x:Id, k:Knd, T:Type. Thm* @i: only members of [k] affect x :T Dsys Thm* & (D:Dsys. Thm* & (@i: only members of [k] affect x :T D Thm* & ( Thm* & (D Thm* & (realizes es.(vartype(i;x) r T) Thm* & (realizes es.& e@i.((x after e) = (x when e) T kind(e) = k Knd) Thm* & (realizes es.& & (kind(e) = k Knd (x after e) = (x when e) T))	[frame-rule1]
Thm* i,a,x:Id, A,T:Type, c:A, P:(ATProp). Thm* @i: ma-single-pre-init1(x;A;c;a;T;x,v.P(x,v)) Dsys Thm* & (D:Dsys. Thm* & (@i: ma-single-pre-init1(x;A;c;a;T;x,v.P(x,v)) D Thm* & ( Thm* & (D Thm* & (realizes es.(vartype(i;x) r A) Thm* & (realizes es.& (e:E. loc(e) = i Id first(e) (x when e) = c A) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = i Id Thm* & (realizes es.& ( Thm* & (realizes es.& (kind(e) = locl(a) Knd (valtype(e) r T)) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = i Id Thm* & (realizes es.& ( Thm* & (realizes es.& (kind(e) = locl(a) Knd P((x when e),val(e))) Thm* & (realizes es.& & ((v:T. P(c,v)) Thm* & (realizes es.& & ( Thm* & (realizes es.& & ((e:E. Thm* & (realizes es.& & ((loc(e) = i Id Thm* & (realizes es.& & ((& kind(e) = locl(a) Knd Thm* & (realizes es.& & ((& (v:T. P((x after e),v)))))	[s-pre-init-rule1]
Thm* i:Id, L:Knd List, x:Id, T:Type. Thm* @i: only members of L affect x :T Dsys Thm* & (D:Dsys. Thm* & (@i: only members of L affect x :T D Thm* & ( Thm* & (D Thm* & (realizes es.(vartype(i;x) r T) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = i Id Thm* & (realizes es.& ( Thm* & (realizes es.& (((x after e) = (x when e) T (kind(e) L)) Thm* & (realizes es.& (& ((kind(e) L) (x after e) = (x when e) T)))	[s-frame-rule]
Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type. Thm* (rcv(l; tg) = k T = B) Thm* Thm* (f:(ABT), c:(AB). Thm* (@source(l): ma-single-sends1(A; Thm* (@source(l): ma-single-sends1(B; Thm* (@source(l): ma-single-sends1(T; Thm* (@source(l): ma-single-sends1(x; Thm* (@source(l): ma-single-sends1(k; Thm* (@source(l): ma-single-sends1(l; Thm* (@source(l): ma-single-sends1(tg; Thm* (@source(l): ma-single-sends1((a,b. if c(a,b) [(f(a,b))] else nil fi)) Thm* ( Dsys Thm* (& (D:Dsys. Thm* (& (@source(l): ma-single-sends1(A; Thm* (& (@source(l): ma-single-sends1(B; Thm* (& (@source(l): ma-single-sends1(T; Thm* (& (@source(l): ma-single-sends1(x; Thm* (& (@source(l): ma-single-sends1(k; Thm* (& (@source(l): ma-single-sends1(l; Thm* (& (@source(l): ma-single-sends1(tg; Thm* (& (@source(l): ma-single-sends1((a,b. if c(a,b) [(f(a,b))] else nil fi) Thm* (& (@source(l): ma-single-sends1() D Thm* (& ( Thm* (& (D Thm* (& (realizes es.(vartype(source(l);x) r A) Thm* (& (realizes es.& (e:E. Thm* (& (realizes es.& (loc(e) = source(l) Id Thm* (& (realizes es.& ( Thm* (& (realizes es.& (kind(e) = k Knd (valtype(e) r B)) Thm* (& (realizes es.& (e:E. kind(e) = rcv(l; tg) Knd (valtype(e) r T)) Thm* (& (realizes es.& (e:E. Thm* (& (realizes es.& (loc(e) = source(l) Id Thm* (& (realizes es.& ( Thm* (& (realizes es.& (kind(e) = k Knd Thm* (& (realizes es.& ( Thm* (& (realizes es.& ((c((x when e),val(e)) Thm* (& (realizes es.& (( Thm* (& (realizes es.& (((e':E. Thm* (& (realizes es.& (((kind(e') = rcv(l; tg) Knd Thm* (& (realizes es.& (((& sender(e') = e E Thm* (& (realizes es.& (((& & (e'':E. Thm* (& (realizes es.& (((& & (kind(e'') = rcv(l; tg) Knd Thm* (& (realizes es.& (((& & ( Thm* (& (realizes es.& (((& & (sender(e'') = e E e'' = e' E) Thm* (& (realizes es.& (((& & val(e') = f((x when e),val(e)) T)) Thm* (& (realizes es.& (& (c((x when e),val(e)) Thm* (& (realizes es.& (& ( Thm* (& (realizes es.& (& ((e':E. Thm* (& (realizes es.& (& ((kind(e') = rcv(l; tg) Knd Thm* (& (realizes es.& (& ((& sender(e') = e E)))))	[conditional-send1-rule]
Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type. Thm* (rcv(l; tg) = k T = B) Thm* Thm* (f:(ABT). Thm* (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; (a,b. [(f(a,b))])) Thm* ( Dsys Thm* (& (D:Dsys. Thm* (& (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; (a,b. [(f(a,b))]) Thm* (& (@source(l): ma-single-sends1() D Thm* (& ( Thm* (& (D Thm* (& (realizes es.(vartype(source(l);x) r A) Thm* (& (realizes es.& (e:E. Thm* (& (realizes es.& (loc(e) = source(l) Id Thm* (& (realizes es.& ( Thm* (& (realizes es.& (kind(e) = k Knd (valtype(e) r B)) Thm* (& (realizes es.& (e:E. kind(e) = rcv(l; tg) Knd (valtype(e) r T)) Thm* (& (realizes es.& (e:E. Thm* (& (realizes es.& (loc(e) = source(l) Id Thm* (& (realizes es.& ( Thm* (& (realizes es.& (kind(e) = k Knd Thm* (& (realizes es.& ( Thm* (& (realizes es.& ((e':E. Thm* (& (realizes es.& ((kind(e') = rcv(l; tg) Knd Thm* (& (realizes es.& ((& sender(e') = e E Thm* (& (realizes es.& ((& & (e'':E. Thm* (& (realizes es.& ((& & (kind(e'') = rcv(l; tg) Knd Thm* (& (realizes es.& ((& & ( Thm* (& (realizes es.& ((& & (sender(e'') = e E e'' = e' E) Thm* (& (realizes es.& ((& & val(e') = f((x when e),val(e)) T))))	[s-unconditional-send1-rule]
Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type, f:(AB(T List)). Thm* (rcv(l; tg) = k T = B) Thm* Thm* @source(l): ma-single-sends1(A; B; T; x; k; l; tg; f) Dsys Thm* & (D:Dsys. Thm* & (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; f) D Thm* & ( Thm* & (D Thm* & (realizes es.(vartype(source(l);x) r A) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = source(l) Id Thm* & (realizes es.& ( Thm* & (realizes es.& (kind(e) = k Knd (valtype(e) r B)) Thm* & (realizes es.& (e:E. kind(e) = rcv(l; tg) Knd (valtype(e) r T)) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = source(l) Id Thm* & (realizes es.& ( Thm* & (realizes es.& (kind(e) = k Knd Thm* & (realizes es.& ( Thm* & (realizes es.& ((L:{e':E\| kind(e') = rcv(l; tg) Knd } List. Thm* & (realizes es.& (((e':E. Thm* & (realizes es.& ((((e' L) Thm* & (realizes es.& ((( Thm* & (realizes es.& (((kind(e') = rcv(l; tg) Knd & sender(e') = e E) Thm* & (realizes es.& ((& (e1,e2:E. e1 before e2 L (e1 <loc e2)) Thm* & (realizes es.& ((& map(e'.val(e');L) = f((x when e),val(e)) T List)))	[s-sends-rule1]
Def spanner(f;T;to;from) Def == (l:Edge(T). f(l) = f(inverse(l))) Def == & (i:\|T\|, l1,l2:Edge(T). Def == & ((l1 to(i)) Def == & ( Def == & ((l2 to(i)) l1 = l2 IdLnk (f(l1)) (f(l2)))	[spanner]
Def bi-tree(T;to;from) Def == bi-graph(T;to;from) Def == & (i,j:\|T\|. Def == & (p:Edge(T) List. Def == & (lconnects(p;i;j) & (q:Edge(T) List. lconnects(q;i;j) q = p)) Def == & (L:\|T\| List. i:\|T\|. (i L)) Def == & \|T\|	[bi-tree]
Def bi-graph(G;to;from) Def == i:\|G\|. Def == (lto(i).destination(l) = i Def == & (G(source(l))) Def == & (l from(source(l))) Def == & (lnk-inv(l) from(i))) Def == & (lfrom(i).source(l) = i Def == & & (G(destination(l))) Def == & & (l to(destination(l))) Def == & & (lnk-inv(l) to(i)))	[bi-graph]
Def ring(R;in;out) Def == (i:\|R\|. Def == ((R(source(in(i)))) & (R(destination(out(i)))) Def == (& source(out(i)) = i Def == (& & destination(in(i)) = i Def == (& & in(destination(out(i))) = out(i) IdLnk Def == (& & out(source(in(i))) = in(i) IdLnk) Def == & (i,j:\|R\|. k:. x.destination(out(x))^k(i) = j Id) Def == & \|R\|	[ring]