{ 
[M:Type 
Type]
n2m:
pMsg(P.M[P]). l2m:Id pMsg(P.M[P]).
Cs0:component(P.M[P]) List. G0:LabeledDAG(pInTransit(P.M[P])).
env:pEnvType(P.M[P]). t:.
let r = pRun(<Cs0, G0>;env;n2m;l2m) in
let info,Cs,G = r t in
x
G.let ev = fst(x) in
((fst(ev)) 
t)
(
m:lg-size(G0). (ev = (fst(lg-label(G0;m)))))
supposing Continuous+(P.M[P]) }
{ Proof }
Definitions occuring in Statement :
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
pInTransit: pInTransit(P.M[P]),
component: component(P.M[P]),
pMsg: pMsg(P.M[P]),
lg-all: xG.P[x],
ldag: LabeledDAG(T),
lg-label: lg-label(g;x),
lg-size: lg-size(g),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
int_seg: {i..j
},
nat: ,
let: let,
spreadn: spread3,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
le: A B,
all: x:A. B[x],
exists: x:A. B[x],
or: P Q,
apply: f a,
function: x:A B[x],
pair: <a, b>,
product: x:A 
B[x],
list: type List,
natural_number: $n,
int: 
,
universe: Type,
equal: s = t
Definitions :
Knd: Knd,
IdLnk: IdLnk,
rationals: 
,
sq_type: SQType(T),
unit: Unit,
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
pi2: snd(t),
add: n + m,
l_member: (x l),
assert: 
b,
System: System(P.M[P]),
guard: {T},
tag-by: zT,
rev_implies: P 
Q,
iff: P 
Q,
fpf-sub: f 
g,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A 
B,
bag: bag(T),
true: True,
fpf-cap: f(x)?z,
length: ||as||,
dep-isect: Error :dep-isect,
bool: 
,
void: Void,
intensional-universe: IType,
es-E-interface: E(X),
lelt: i j < k,
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
pCom: pCom(P.M[P]),
atom: Atom$n,
limited-type: LimitedType,
real: 
,
grp_car: |g|,
subtype: S T,
top: Top,
is-dag: is-dag(g),
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
less_than: a < b,
uiff: uiff(P;Q),
union: left + right,
labeled-graph: LabeledGraph(T),
apply: f a,
set: {x:A| B[x]} ,
implies: P Q,
false: False,
not: 
A,
pEnvType: pEnvType(T.M[T]),
ldag: LabeledDAG(T),
component: component(P.M[P]),
list: type List,
pMsg: pMsg(P.M[P]),
let: let,
lambda: 
x.A[x],
pRun: pRun(S0;env;nat2msg;loc2msg),
uimplies: b supposing a,
so_lambda: 
x.t[x],
spreadn: spread3,
strong-type-continuous: Continuous+(T.F[T]),
uall: [x:A]. B[x],
universe: Type,
nat: ,
function: x:A B[x],
isect: x:A. B[x],
ext-eq: A 
B,
and: P 
Q,
subtype_rel: A r B,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
pair: <a, b>,
lg-label: lg-label(g;x),
pi1: fst(t),
Id: Id,
int: ,
product: x:A B[x],
equal: s = t,
lg-size: lg-size(g),
natural_number: $n,
int_seg: {i..j},
exists: x:A. B[x],
le: A B,
or: P Q,
lg-all: xG.P[x],
spread: spread def,
so_lambda: x y.t[x; y],
CollapseTHENA: Error :CollapseTHENA,
prop: 
,
member: t T,
all: x:A. B[x],
so_apply: x[s],
pInTransit: pInTransit(P.M[P]),
AssertBY: Error :AssertBY,
Auto: Error :Auto,
RepUR: Error :RepUR,
tactic: Error :tactic,
D: Error :D,
MaAuto: Error :MaAuto,
fpf-dom: x dom(f),
nat_plus: 
,
pRunType: pRunType(T.M[T]),
fulpRunType: fulpRunType(T.M[T]),
suptype: suptype(S; T),
RepeatFor: Error :RepeatFor,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
bnot: 
b,
lg-is-source: lg-is-source(g;i),
bor: p q,
band: p q,
bimplies: p q,
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
eq_str: Error :eq_str,
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_type: eq_type(T;T'),
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
infix_ap: x f y,
grp_blt: a < b,
set_blt: a < b,
null: null(as),
eq_int: (i =
j),
le_int: i z j,
lt_int: i <z j,
eq_bool: p =b q,
btrue: tt,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
bfalse: ff,
SplitOn: Error :SplitOn,
lg-remove: lg-remove(g;n),
skip: Error :skip,
Com: Com(P.M[P]),
lg-in-edges: lg-in-edges(g;x),
list_accum: list_accum(x,a.f[x; a];y;l),
deliver-msg-to-comp: deliver-msg-to-comp(t;m;x;S;C),
Process: Process(P.M[P]),
process: process(P.M[P];P.E[P]),
corec: corec(T.F[T]),
sqequal: s ~ t,
Process-apply: Process-apply(P;m),
cons: [car / cdr],
lg-append: lg-append(g1;g2),
add-cause: add-cause(ev;ext),
pExt: pExt(P.M[P]),
cand: A c B,
es-causl: (e < e'),
es-locl: (e <loc e'),
decidable: Dec(P),
lg-edge: lg-edge(g;a;b),
path-goes-thru: x-f*-y thru i,
cut-order: a (X;f) b,
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
same-thread: same-thread(es;p;e;e'),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
es-fset-loc: i locs(s),
existse-between3: e(e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
alle-between2: e[e1,e2].P[e],
existse-between1: e[e1,e2).P[e],
alle-between1: e[e1,e2).P[e],
alle-le: ee'.P[e],
alle-lt: e<e'.P[e],
existse-le: ee'.P[e],
existse-before: e<e'.P[e],
es-causle: e c e',
es-le: e loc e' ,
cs-precondition: state s may consider v in inning i,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
l_disjoint: l_disjoint(T;l1;l2),
fset-closed: (s closed under fs),
f-subset: xs ys,
fset-member: a s,
p-outcome: Outcome,
i-closed: i-closed(I),
i-finite: i-finite(I),
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
fun-connected: y is f*(x),
l_all: (xL.P[x]),
l_exists: (xL. P[x]),
squash: 
T,
prime: prime(a),
reducible: reducible(a),
inject: Inj(A;B;f),
l_contains: A B,
grp_lt: a < b,
set_lt: a <p b,
set_leq: a b,
assoced: a ~ b,
divides: b | a,
Repeat: Error :Repeat,
Subst': Error :Subst',
subtract: n - m,
BHyp: Error :BHyp,
com-kind: com-kind(c),
token: "$token",
atom: Atom,
deliver-msg: deliver-msg(t;m;x;Cs;L),
create-component: create-component(t;P;x;Cs;L),
comm-msg: comm-msg(c),
nil: [],
it: 
,
THENL_v2: Error :THENL,
THENL_cons: Error :THENL_cons,
THENL_cons: Error :THENL_nil,
Unfold: Error :Unfold
Lemmas :
comm-msg_wf,
int_subtype_base,
create-component_wf,
assert_of_eq_atom,
eq_atom_wf,
com-kind_wf,
deliver-msg_wf,
ifthenelse_wf,
bfalse_wf,
decidable__le,
lg-all_wf,
lg-all-map,
Error :dep-isect_wf,
lg-all-append,
Process_wf,
pExt_wf,
add-cause_wf,
Process-apply_wf,
eq_id_wf,
not_functionality_wrt_uiff,
assert-eq-id,
uall_wf,
deliver-msg-to-comp_wf,
list_accum_wf,
uiff_inversion,
lg-all-remove,
lg-remove_wf_dag,
le_int_wf,
lt_int_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
bool_subtype_base,
assert_of_lt_int,
bool_cases,
bool_wf,
lg-is-source_wf_dag,
bnot_wf,
assert_wf,
not_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
iff_weakening_uiff,
eqtt_to_assert,
subtype_rel_function,
nat_plus_wf,
pRun_wf2,
pRunType_wf,
fulpRunType_wf,
subtype_rel_self,
int_seg_properties,
subtype_rel_simple_product,
pCom_wf,
pInTransit_wf,
top_wf,
member_wf,
subtype_rel_wf,
lg-label_wf_dag,
Id_wf,
pi1_wf_top,
nat_wf,
lg-size_wf_dag,
int_seg_wf,
le_wf,
strong-type-continuous_wf,
pMsg_wf,
component_wf,
ldag_wf,
pEnvType_wf,
pRun_wf,
lg-size_wf,
intensional-universe_wf,
false_wf,
is-dag_wf,
labeled-graph_wf,
subtype_rel-ldag,
pRun-System-invariant,
System_wf,
lg-all_wf_dag,
nat_properties,
do-chosen-command_wf,
unit_wf,
pi2_wf,
subtype_base_sq
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]). \mforall{}Cs0:component(P.M[P]) List.
\mforall{}G0:LabeledDAG(pInTransit(P.M[P])). \mforall{}env:pEnvType(P.M[P]). \mforall{}t:\mBbbN{}.
let r = pRun(<Cs0, G0>env;n2m;l2m) in
let info,Cs,G = r t in
\mforall{}x\mmember{}G.let ev = fst(x) in
((fst(ev)) \mleq{} t) \mvee{} (\mexists{}m:\mBbbN{}lg-size(G0). (ev = (fst(lg-label(G0;m)))))
supposing Continuous+(P.M[P])
Date html generated:
2011_08_16-PM-07_03_45
Last ObjectModification:
2011_06_18-AM-11_17_13
Home
Index