Nuprl - mb_event_system_7 Citations of IdLnk

mb event system 7 Sections EventSystems Doc

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Def IdLnk == Id

is mentioned by

Thm* T:(Id), to,from:(|T|(IdLnk List)), f:(Edge(T)).
Thm* bi-tree(T;to;from)
Thm*
Thm* spanner(f;T;to;from)
Thm*
Thm* (i,j:|T|.
Thm* (spanner-root(f;T;to;from;i)  spanner-root(f;T;to;from;j)  i = j) [spanner-root-unique]

Thm* T:(Id), to,from:(|T|(IdLnk List)), f:(Edge(T)).
Thm* bi-tree(T;to;from)
Thm*
Thm* spanner(f;T;to;from)  (i:|T|. spanner-root(f;T;to;from;i)) [spanner-root-exists]

Thm* T:(Id), to,from:(|T|(IdLnk List)), f:(Edge(T)).
Thm* bi-graph(T;to;from)  spanner(f;T;to;from)  Prop [spanner_wf]

Thm* T:(Id), to,from:(|T|(IdLnk List)).
Thm* bi-tree(T;to;from)  (n:. p:Edge(T) List. lpath(p)  ||p||n) [bi-tree-diameter]

Thm* G:(Id), to,from:(|G|(IdLnk List)). bi-tree(G;to;from)  Prop [bi-tree_wf]

Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|.
Thm* bi-graph(G;to;from)  ((inverse(e)  from(i))  destination(e) = i) [edge-inv-from]

Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|.
Thm* bi-graph(G;to;from)  ((inverse(e)  to(i))  source(e) = i) [edge-inv-to]

Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|.
Thm* bi-graph(G;to;from)  ((e  from(i))  source(e) = i) [edge-from]

Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|.
Thm* bi-graph(G;to;from)  ((e  to(i))  destination(e) = i) [edge-to]

Thm* G:(Id), to,from:(|G|(IdLnk List)), l:Edge(G).
Thm* bi-graph(G;to;from)  inverse(l)  Edge(G) [bi-graph-inv_wf]

Thm* G:(Id), to,from:(|G|(IdLnk List)), i:|G|.
Thm* bi-graph(G;to;from)  from(i)  Edge(G) List [bi-graph-from_wf]

Thm* G:(Id), to,from:(|G|(IdLnk List)), i:|G|.
Thm* bi-graph(G;to;from)  to(i)  Edge(G) List [bi-graph-to_wf]

Thm* T:(Id), to,from:(|T|(IdLnk List)), u:Edge(T).
Thm* bi-graph(T;to;from)  destination(u)  |T| [dst-edge]

Thm* T:(Id), to,from:(|T|(IdLnk List)), u:Edge(T).
Thm* bi-graph(T;to;from)  source(u)  |T| [src-edge]

Thm* G:(Id), to,from:(|G|(IdLnk List)), l:Edge(G).
Thm* bi-graph(G;to;from)  lnk-inv(l)  Edge(G) [inv-is-edge]

Thm* G:(Id), to,from:(|G|(IdLnk List)). bi-graph(G;to;from)  Prop [bi-graph_wf]

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), uid:(|R|), out,in:(|R|IdLnk).
Thm* ring(R;in;out)
Thm*
Thm* Inj(|R|; ; uid)  d-feasible(loc.(ring-leader1(loc;R;uid;out;in))) [ring-leader1__feasible]

Thm* loc:Id, R:(Id), uid:(|R|), out,in:(|R|IdLnk).
Thm* ring(R;in;out)
Thm*
Thm* Inj(|R|; ; uid)  ring-leader1(loc;R;uid;out;in)  MsgA List [ring-leader1_wf]

Thm* loc:Id, R:(Id), uid:(|R|), out,in:(|R|IdLnk).
Thm* ring(R;in;out)
Thm*
Thm* Inj(|R|; ; uid)  (A,Bring-leader1(loc;R;uid;out;in).A ||+ B) [ring-leader1__compatible]

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)  i = p(j)  d(i;p(j)) = d(i;j)-1 [rdist-rprev]

Thm* R:(Id), in,out:(|R|IdLnk).
Thm* ring(R;in;out)  (i,j:|R|. n(i) = n(j)  i = j) [rnext-one-one]

Thm* R:(Id), in,out:(|R|IdLnk), j:|R|. ring(R;in;out)  n(p(j)) = j [rnext-rprev]

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* R:(Id), in,out:(|R|IdLnk), i,j:|R|. ring(R;in;out)  d(i;j)   [rdist_wf]

Thm* R:(Id), in,out:(|R|IdLnk), i:|R|. ring(R;in;out)  p(i)  |R| [rprev_wf]

Thm* R:(Id), in,out:(|R|IdLnk), i:|R|. ring(R;in;out)  n(i)  |R| [rnext_wf]

Thm* R:(Id), in,out:(|R|IdLnk). ring(R;in;out)  Prop [ring_wf]

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:Id, f:(AT), tg:Id, l:IdLnk, x:Id.
Thm* "done" = x  A  T  d-feasible(loc.(send-once(loc;T;A;a;f;tg;l;x))) [send-once__feasible]

Thm* loc:Id, T,A:Type, a:Id, f:(AT), tg:Id, l:IdLnk, x:Id.
Thm* "done" = x  A  T  send-once(loc;T;A;a;f;tg;l;x)  MsgA List [send-once_wf]

Thm* loc:Id, T,A:Type, a:Id, f:(AT), tg:Id, l:IdLnk, x:Id.
Thm* "done" = x  A  T  (A,Bsend-once(loc;T;A;a;f;tg;l;x).A ||+ B) [send-once__compatible]

Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List,
Thm* k1:Knd, l1:IdLnk, d1:x:Id fp-> Type, d2:a:Knd fp-> Type, f1:(IdTop) List.
Thm* ds || d1
Thm*
Thm* da || d2
Thm*
Thm* <k,l> = <k1,l1>
Thm*
Thm* ma-single-sends(ds; da; k; l; f) ||+ ma-single-sends(d1; d2; k1; l1; f1) [ma-single-sends-ma-single-sends-compatible]

Thm* l:IdLnk, tg:Id, L:Top, x:Id, t,v:Top.
Thm* x : t initially x = v ||+ only L sends on (l with tg) [ma-single-init-ma-single-sframe-compatible]

Thm* l:IdLnk, tg:Id, L:Top, x:Id, L1,t:Top.
Thm* only members of L1 affect x :t ||+ only L sends on (l with tg) [ma-single-frame-ma-single-sframe-compatible]

Thm* x:Id, k:Knd, ds:x:Id fp-> Top, da:a:Knd fp-> Top, f:Top, l:IdLnk, tg:Id,
Thm* L:Top. ma-single-effect(ds; da; k; x; f) ||+ only L sends on (l with tg) [ma-single-effect-ma-single-sframe-compatible]

Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Top, f:(IdTop) List,
Thm* x:Id, t:Type, v:t.
Thm* ds || x : t  x : t initially x = v ||+ ma-single-sends(ds; da; k; l; f) [ma-single-init-ma-single-sends-compatible]

Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Top, f:(IdTop) List,
Thm* x:Id, t:Type, v:t.
Thm* ds || x : t  ma-single-sends(ds; da; k; l; f) ||+ x : t initially x = v [ma-single-sends-ma-single-init-compatible]

Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Top, f:(IdTop) List,
Thm* x:Id, L:Top, t:Type.
Thm* ds || x : t
Thm*
Thm* only members of L affect x :t ||+ ma-single-sends(ds; da; k; l; f) [ma-single-frame-ma-single-sends-compatible]

Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Top, f:(IdTop) List,
Thm* x:Id, L:Top, t:Type.
Thm* ds || x : t
Thm*
Thm* ma-single-sends(ds; da; k; l; f) ||+ only members of L affect x :t [ma-single-sends-ma-single-frame-compatible]

Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List,
Thm* l1:IdLnk, tg:Id, L:Knd List.
Thm* (l = l1  (tg  map(p.1of(p);f))  (k  L))
Thm*
Thm* ma-single-sends(ds; da; k; l; f) ||+ only L sends on (l1 with tg) [ma-single-sends-ma-single-sframe-compatible]

Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List,
Thm* x:Id, k1:Knd, d1:x:Id fp-> Type, d2:a:Knd fp-> Type, f1:Top.
Thm* ds || d1
Thm*
Thm* da || d2
Thm*
Thm* ma-single-effect(d1; d2; k1; x; f1) ||+ ma-single-sends(ds; da; k; l; f) [ma-single-effect-ma-single-sends-compatible]

Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List,
Thm* x:Id, k1:Knd, d1:x:Id fp-> Type, d2:a:Knd fp-> Type, f1:Top.
Thm* ds || d1
Thm*
Thm* da || d2
Thm*
Thm* ma-single-sends(ds; da; k; l; f) ||+ ma-single-effect(d1; d2; k1; x; f1) [ma-single-sends-ma-single-effect-compatible]

Thm* a:Id, T:Type, ds:x:Id fp-> Top, P:Top, l:IdLnk, tg:Id, L:Top.
Thm* (with ds: ds
Thm* (action a:T
Thm* (precondition a(v) is
Thm* (P s v) ||+ only L sends on (l with tg) [ma-single-pre-ma-single-sframe-compatible]

Thm* a:Id, T:Type, ds:x:Id fp-> Type, P:Top, k:Knd, l:IdLnk, d1:x:Id fp-> Type,
Thm* da:a:Knd fp-> Type, f:(IdTop) List.
Thm* ds || d1
Thm*
Thm* locl(a) : T || da
Thm*
Thm* ma-single-sends(d1; da; k; l; f) ||+ (with ds: ds
Thm* maction a:T
Thm* mprecondition a(v) is
Thm* mP s v) [ma-single-sends-ma-single-pre-compatible]

Thm* a:Id, T:Type, ds:x:Id fp-> Type, P:Top, k:Knd, l:IdLnk, d1:x:Id fp-> Type,
Thm* da:a:Knd fp-> Type, f:(IdTop) List.
Thm* ds || d1
Thm*
Thm* locl(a) : T || da
Thm*
Thm* (with ds: ds
Thm* (action a:T
Thm* (precondition a(v) is
Thm* (P s v) ||+ ma-single-sends(d1; da; k; l; f) [ma-single-pre-ma-single-sends-compatible]

Thm* a:Id, T:Top, ds:x:Id fp-> Top, P:Top, init:x:Id fp-> Top, l:IdLnk, tg:Id,
Thm* L:Knd List.
Thm* (with ds: ds
Thm* (init: init
Thm* action a:T
Thm* aprecondition a(v) is
Thm* aP) ||+ only L sends on (l with tg) [ma-single-pre-init-ma-single-sframe-compatible]

Thm* a:Id, T:Type, ds:x:Id fp-> Type, P:Top, init:x:Id fp-> Top, k:Knd,
Thm* l:IdLnk, d1:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List.
Thm* ds || d1
Thm*
Thm* locl(a) : T || da
Thm*
Thm* (with ds: ds
Thm* (init: init
Thm* action a:T
Thm* aprecondition a(v) is
Thm* aP) ||+ ma-single-sends(d1; da; k; l; f) [ma-single-pre-init-ma-single-sends-compatible]

Thm* L:Knd List, l:IdLnk, tg:Id.
Thm* @source(l): only L sends on (l with tg)  Dsys
Thm* & (D:Dsys.
Thm* & (@source(l): only L sends on (l with tg)  D
Thm* & (
Thm* & (D
Thm* & (realizes es.e:E.
Thm* & (realizes es.loc(e) = destination(l)  Id
Thm* & (realizes es.
Thm* & (realizes es.kind(e) = rcv(l; tg)  Knd  (kind(sender(e))  L)) [better-sframe-rule]

Thm* i:Id, L:Knd List, l:IdLnk, tg:Id.
Thm* @i: only L sends on (l with tg)  Dsys
Thm* & (D:Dsys.
Thm* & (@i: only L sends on (l with tg)  D
Thm* & (
Thm* & (D
Thm* & (realizes es.e:E.
Thm* & (realizes es.loc(e) = i  Id  null(sends(l,tg,e))  (kind(e)  L)) [s-sframe-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 Edge(G) == {l:IdLnk| i:|G|. (l  from(i)) } [bi-graph-edge]

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: mb event system 1 mb event system 2 mb event system 3 mb event system 4 mb event system 5 mb event system 6

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mb event system 7 Sections EventSystems Doc

Thm* T:(Id), to,from:(\|T\|(IdLnk List)), f:(Edge(T)). Thm* bi-tree(T;to;from) Thm* Thm* spanner(f;T;to;from) Thm* Thm* (i,j:\|T\|. Thm* (spanner-root(f;T;to;from;i) spanner-root(f;T;to;from;j) i = j)	[spanner-root-unique]
Thm* T:(Id), to,from:(\|T\|(IdLnk List)), f:(Edge(T)). Thm* bi-tree(T;to;from) Thm* Thm* spanner(f;T;to;from) (i:\|T\|. spanner-root(f;T;to;from;i))	[spanner-root-exists]
Thm* T:(Id), to,from:(\|T\|(IdLnk List)), f:(Edge(T)). Thm* bi-graph(T;to;from) spanner(f;T;to;from) Prop	[spanner_wf]
Thm* T:(Id), to,from:(\|T\|(IdLnk List)). Thm* bi-tree(T;to;from) (n:. p:Edge(T) List. lpath(p) \|\|p\|\|n)	[bi-tree-diameter]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)). bi-tree(G;to;from) Prop	[bi-tree_wf]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), e:Edge(G), i:\|G\|. Thm* bi-graph(G;to;from) ((inverse(e) from(i)) destination(e) = i)	[edge-inv-from]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), e:Edge(G), i:\|G\|. Thm* bi-graph(G;to;from) ((inverse(e) to(i)) source(e) = i)	[edge-inv-to]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), e:Edge(G), i:\|G\|. Thm* bi-graph(G;to;from) ((e from(i)) source(e) = i)	[edge-from]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), e:Edge(G), i:\|G\|. Thm* bi-graph(G;to;from) ((e to(i)) destination(e) = i)	[edge-to]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), l:Edge(G). Thm* bi-graph(G;to;from) inverse(l) Edge(G)	[bi-graph-inv_wf]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), i:\|G\|. Thm* bi-graph(G;to;from) from(i) Edge(G) List	[bi-graph-from_wf]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), i:\|G\|. Thm* bi-graph(G;to;from) to(i) Edge(G) List	[bi-graph-to_wf]
Thm* T:(Id), to,from:(\|T\|(IdLnk List)), u:Edge(T). Thm* bi-graph(T;to;from) destination(u) \|T\|	[dst-edge]
Thm* T:(Id), to,from:(\|T\|(IdLnk List)), u:Edge(T). Thm* bi-graph(T;to;from) source(u) \|T\|	[src-edge]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), l:Edge(G). Thm* bi-graph(G;to;from) lnk-inv(l) Edge(G)	[inv-is-edge]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)). bi-graph(G;to;from) Prop	[bi-graph_wf]
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), uid:(\|R\|), out,in:(\|R\|IdLnk). Thm* ring(R;in;out) Thm* Thm* Inj(\|R\|; ; uid) d-feasible(loc.(ring-leader1(loc;R;uid;out;in)))	[ring-leader1__feasible]
Thm* loc:Id, R:(Id), uid:(\|R\|), out,in:(\|R\|IdLnk). Thm* ring(R;in;out) Thm* Thm* Inj(\|R\|; ; uid) ring-leader1(loc;R;uid;out;in) MsgA List	[ring-leader1_wf]
Thm* loc:Id, R:(Id), uid:(\|R\|), out,in:(\|R\|IdLnk). Thm* ring(R;in;out) Thm* Thm* Inj(\|R\|; ; uid) (A,Bring-leader1(loc;R;uid;out;in).A \|\|+ B)	[ring-leader1__compatible]
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) i = p(j) d(i;p(j)) = d(i;j)-1	[rdist-rprev]
Thm* R:(Id), in,out:(\|R\|IdLnk). Thm* ring(R;in;out) (i,j:\|R\|. n(i) = n(j) i = j)	[rnext-one-one]
Thm* R:(Id), in,out:(\|R\|IdLnk), j:\|R\|. ring(R;in;out) n(p(j)) = j	[rnext-rprev]
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* R:(Id), in,out:(\|R\|IdLnk), i,j:\|R\|. ring(R;in;out) d(i;j)	[rdist_wf]
Thm* R:(Id), in,out:(\|R\|IdLnk), i:\|R\|. ring(R;in;out) p(i) \|R\|	[rprev_wf]
Thm* R:(Id), in,out:(\|R\|IdLnk), i:\|R\|. ring(R;in;out) n(i) \|R\|	[rnext_wf]
Thm* R:(Id), in,out:(\|R\|IdLnk). ring(R;in;out) Prop	[ring_wf]
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:Id, f:(AT), tg:Id, l:IdLnk, x:Id. Thm* "done" = x A T d-feasible(loc.(send-once(loc;T;A;a;f;tg;l;x)))	[send-once__feasible]
Thm* loc:Id, T,A:Type, a:Id, f:(AT), tg:Id, l:IdLnk, x:Id. Thm* "done" = x A T send-once(loc;T;A;a;f;tg;l;x) MsgA List	[send-once_wf]
Thm* loc:Id, T,A:Type, a:Id, f:(AT), tg:Id, l:IdLnk, x:Id. Thm* "done" = x A T (A,Bsend-once(loc;T;A;a;f;tg;l;x).A \|\|+ B)	[send-once__compatible]
Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List, Thm* k1:Knd, l1:IdLnk, d1:x:Id fp-> Type, d2:a:Knd fp-> Type, f1:(IdTop) List. Thm* ds \|\| d1 Thm* Thm* da \|\| d2 Thm* Thm* <k,l> = <k1,l1> Thm* Thm* ma-single-sends(ds; da; k; l; f) \|\|+ ma-single-sends(d1; d2; k1; l1; f1)	[ma-single-sends-ma-single-sends-compatible]
Thm* l:IdLnk, tg:Id, L:Top, x:Id, t,v:Top. Thm* x : t initially x = v \|\|+ only L sends on (l with tg)	[ma-single-init-ma-single-sframe-compatible]
Thm* l:IdLnk, tg:Id, L:Top, x:Id, L1,t:Top. Thm* only members of L1 affect x :t \|\|+ only L sends on (l with tg)	[ma-single-frame-ma-single-sframe-compatible]
Thm* x:Id, k:Knd, ds:x:Id fp-> Top, da:a:Knd fp-> Top, f:Top, l:IdLnk, tg:Id, Thm* L:Top. ma-single-effect(ds; da; k; x; f) \|\|+ only L sends on (l with tg)	[ma-single-effect-ma-single-sframe-compatible]
Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Top, f:(IdTop) List, Thm* x:Id, t:Type, v:t. Thm* ds \|\| x : t x : t initially x = v \|\|+ ma-single-sends(ds; da; k; l; f)	[ma-single-init-ma-single-sends-compatible]
Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Top, f:(IdTop) List, Thm* x:Id, t:Type, v:t. Thm* ds \|\| x : t ma-single-sends(ds; da; k; l; f) \|\|+ x : t initially x = v	[ma-single-sends-ma-single-init-compatible]
Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Top, f:(IdTop) List, Thm* x:Id, L:Top, t:Type. Thm* ds \|\| x : t Thm* Thm* only members of L affect x :t \|\|+ ma-single-sends(ds; da; k; l; f)	[ma-single-frame-ma-single-sends-compatible]
Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Top, f:(IdTop) List, Thm* x:Id, L:Top, t:Type. Thm* ds \|\| x : t Thm* Thm* ma-single-sends(ds; da; k; l; f) \|\|+ only members of L affect x :t	[ma-single-sends-ma-single-frame-compatible]
Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List, Thm* l1:IdLnk, tg:Id, L:Knd List. Thm* (l = l1 (tg map(p.1of(p);f)) (k L)) Thm* Thm* ma-single-sends(ds; da; k; l; f) \|\|+ only L sends on (l1 with tg)	[ma-single-sends-ma-single-sframe-compatible]
Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List, Thm* x:Id, k1:Knd, d1:x:Id fp-> Type, d2:a:Knd fp-> Type, f1:Top. Thm* ds \|\| d1 Thm* Thm* da \|\| d2 Thm* Thm* ma-single-effect(d1; d2; k1; x; f1) \|\|+ ma-single-sends(ds; da; k; l; f)	[ma-single-effect-ma-single-sends-compatible]
Thm* k:Knd, l:IdLnk, ds:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List, Thm* x:Id, k1:Knd, d1:x:Id fp-> Type, d2:a:Knd fp-> Type, f1:Top. Thm* ds \|\| d1 Thm* Thm* da \|\| d2 Thm* Thm* ma-single-sends(ds; da; k; l; f) \|\|+ ma-single-effect(d1; d2; k1; x; f1)	[ma-single-sends-ma-single-effect-compatible]
Thm* a:Id, T:Type, ds:x:Id fp-> Top, P:Top, l:IdLnk, tg:Id, L:Top. Thm* (with ds: ds Thm* (action a:T Thm* (precondition a(v) is Thm* (P s v) \|\|+ only L sends on (l with tg)	[ma-single-pre-ma-single-sframe-compatible]
Thm* a:Id, T:Type, ds:x:Id fp-> Type, P:Top, k:Knd, l:IdLnk, d1:x:Id fp-> Type, Thm* da:a:Knd fp-> Type, f:(IdTop) List. Thm* ds \|\| d1 Thm* Thm* locl(a) : T \|\| da Thm* Thm* ma-single-sends(d1; da; k; l; f) \|\|+ (with ds: ds Thm* maction a:T Thm* mprecondition a(v) is Thm* mP s v)	[ma-single-sends-ma-single-pre-compatible]
Thm* a:Id, T:Type, ds:x:Id fp-> Type, P:Top, k:Knd, l:IdLnk, d1:x:Id fp-> Type, Thm* da:a:Knd fp-> Type, f:(IdTop) List. Thm* ds \|\| d1 Thm* Thm* locl(a) : T \|\| da Thm* Thm* (with ds: ds Thm* (action a:T Thm* (precondition a(v) is Thm* (P s v) \|\|+ ma-single-sends(d1; da; k; l; f)	[ma-single-pre-ma-single-sends-compatible]
Thm* a:Id, T:Top, ds:x:Id fp-> Top, P:Top, init:x:Id fp-> Top, l:IdLnk, tg:Id, Thm* L:Knd List. Thm* (with ds: ds Thm* (init: init Thm* action a:T Thm* aprecondition a(v) is Thm* aP) \|\|+ only L sends on (l with tg)	[ma-single-pre-init-ma-single-sframe-compatible]
Thm* a:Id, T:Type, ds:x:Id fp-> Type, P:Top, init:x:Id fp-> Top, k:Knd, Thm* l:IdLnk, d1:x:Id fp-> Type, da:a:Knd fp-> Type, f:(IdTop) List. Thm* ds \|\| d1 Thm* Thm* locl(a) : T \|\| da Thm* Thm* (with ds: ds Thm* (init: init Thm* action a:T Thm* aprecondition a(v) is Thm* aP) \|\|+ ma-single-sends(d1; da; k; l; f)	[ma-single-pre-init-ma-single-sends-compatible]
Thm* L:Knd List, l:IdLnk, tg:Id. Thm* @source(l): only L sends on (l with tg) Dsys Thm* & (D:Dsys. Thm* & (@source(l): only L sends on (l with tg) D Thm* & ( Thm* & (D Thm* & (realizes es.e:E. Thm* & (realizes es.loc(e) = destination(l) Id Thm* & (realizes es. Thm* & (realizes es.kind(e) = rcv(l; tg) Knd (kind(sender(e)) L))	[better-sframe-rule]
Thm* i:Id, L:Knd List, l:IdLnk, tg:Id. Thm* @i: only L sends on (l with tg) Dsys Thm* & (D:Dsys. Thm* & (@i: only L sends on (l with tg) D Thm* & ( Thm* & (D Thm* & (realizes es.e:E. Thm* & (realizes es.loc(e) = i Id null(sends(l,tg,e)) (kind(e) L))	[s-sframe-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 Edge(G) == {l:IdLnk\| i:\|G\|. (l from(i)) }	[bi-graph-edge]
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]