{ 
[M:Type 
Type]
n2m:
pMsg(P.M[P]). l2m:Id pMsg(P.M[P]). S0:System(P.M[P]).
env:pEnvType(P.M[P]).
let r = pRun(S0;env;n2m;l2m) in
e:runEvents(r)
(((fst(fst(run-info(r;e)))) < run-event-step(e))
(
m:lg-size(snd(S0))
((fst(run-info(r;e))) = (fst(lg-label(snd(S0);m))))))
supposing Continuous+(P.M[P]) }
{ Proof }
Definitions occuring in Statement :
run-event-step: run-event-step(e),
runEvents: runEvents(r),
run-info: run-info(r;e),
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
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,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
all: x:A. B[x],
exists: x:A. B[x],
or: P Q,
less_than: a < b,
function: x:A B[x],
product: x:A 
B[x],
natural_number: $n,
int: 
,
universe: Type,
equal: s = t
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
strong-type-continuous: Continuous+(T.F[T]),
so_apply: x[s],
all: x:A. B[x],
System: System(P.M[P]),
let: let,
pi1: fst(t),
run-event-step: run-event-step(e),
pi2: snd(t),
member: t 
T,
ext-eq: A 
B,
and: P 
Q,
so_lambda: 
x.t[x],
top: Top,
subtype: S 
T,
squash: 
T,
true: True,
nat: ,
Id: Id,
ldag: LabeledDAG(T),
spreadn: spread3,
pRun: pRun(S0;env;nat2msg;loc2msg),
or: P Q,
le: A 
B,
exists: x:A. B[x],
int_seg: {i..j},
assert: 
b,
is-run-event: is-run-event(r;t;x),
run-info: run-info(r;e),
implies: P 
Q,
outl: outl(x),
ycomb: Y,
ifthenelse: if b then t else f fi ,
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
band: p 
q,
isl: isl(x),
btrue: tt,
bfalse: ff,
prop: 
,
false: False,
not: 
A,
fulpRunType: fulpRunType(T.M[T]),
lelt: i j < k,
guard: {T},
runEvents: runEvents(r),
decidable: Dec(P),
sq_stable: SqStable(P),
pInTransit: pInTransit(P.M[P]),
lg-all: xG.P[x],
lg-is-source: lg-is-source(g;i),
bool: 
,
unit: Unit,
iff: P 
Q,
sq_type: SQType(T),
it: 
Lemmas :
pRun-intransit-invariant,
nat_wf,
pRun_wf2,
decidable__assert,
is-run-event_wf,
pi1_wf_top,
Id_wf,
pi2_wf,
sq_stable__assert,
runEvents_wf,
pEnvType_wf,
System_wf,
pMsg_wf,
strong-type-continuous_wf,
eq_int_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
false_wf,
not_wf,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
pRun_wf,
subtype_rel_function,
unit_wf,
int_seg_wf,
nat_properties,
top_wf,
ldag_wf,
pInTransit_wf,
le_wf,
subtype_rel_simple_product,
subtype_rel_self,
fulpRunType_wf,
lg-is-source_wf_dag,
lt_int_wf,
lg-size_wf_dag,
lg-label_wf_dag,
eq_atom_wf,
com-kind_wf,
assert_of_eq_atom,
assert_witness,
decidable__lt,
lg-size_wf,
is-dag_wf,
subtype_base_sq,
product_subtype_base,
int_subtype_base,
atom2_subtype_base,
subtype_rel-ldag,
component_wf,
lg-all_wf,
le_int_wf,
bool_cases,
bool_subtype_base,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
squash_wf,
true_wf
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]). \mforall{}S0:System(P.M[P]). \mforall{}env:pEnvType(P.M[P]).
let r = pRun(S0;env;n2m;l2m) in
\mforall{}e:runEvents(r)
(((fst(fst(run-info(r;e)))) < run-event-step(e))
\mvee{} (\mexists{}m:\mBbbN{}lg-size(snd(S0)). ((fst(run-info(r;e))) = (fst(lg-label(snd(S0);m))))))
supposing Continuous+(P.M[P])
Date html generated:
2011_08_16-PM-07_03_59
Last ObjectModification:
2011_06_18-AM-11_17_24
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