{ 
[M:Type 
Type]
S0:InitialSystem(P.M[P]). n2m:
pMsg(P.M[P]). l2m:Id pMsg(P.M[P]).
env:pEnvType(P.M[P]).
let r = pRun(S0;env;n2m;l2m) in
reliable-env(env; r)
(tn:run-msg-commands(r)
e:runEvents(r)
let t,n = tn
in (run-info(r;e)
= intransit-to-info(n2m;l2m;r;env;run-event-step(e);...))
(run-event-loc(e) = (fst(snd(run-command(r;t;n))))))
supposing Continuous+(P.M[P]) }
{ Proof }
Definitions occuring in Statement :
intransit-to-info: intransit-to-info(n2m;l2m;r;env;t;lbl),
run-msg-commands: run-msg-commands(r),
run-command: run-command(r;t;n),
reliable-env: reliable-env(env; r),
InitialSystem: InitialSystem(P.M[P]),
run-event-step: run-event-step(e),
run-event-loc: run-event-loc(e),
runEvents: runEvents(r),
run-info: run-info(r;e),
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
pMsg: pMsg(P.M[P]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
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],
implies: P Q,
and: P Q,
function: x:A B[x],
spread: spread def,
product: x:A 
B[x],
int: 
,
universe: Type,
equal: s = t
Definitions :
false: False,
prop: 
,
true: True,
squash: 
T,
so_lambda: 
x.t[x],
not: 
A,
le: A 
B,
and: P Q,
implies: P Q,
all: x:A. B[x],
member: t 
T,
nat: ,
so_apply: x[s],
run-command-node: run-command-node(r;t;n),
pRunType: pRunType(T.M[T]),
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
ycomb: Y,
pRun: pRun(S0;env;nat2msg;loc2msg),
cand: A c B,
uimplies: b supposing a,
lelt: i j < k,
int_seg: {i..j
},
let: let,
spreadn: spread3,
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
pi2: snd(t),
rev_implies: P 
Q,
iff: P Q,
create-component: create-component(t;P;x;Cs;L),
ldag: LabeledDAG(T),
fulpRunType: fulpRunType(T.M[T]),
subtype: S 
T,
nat_plus: 
,
top: Top,
pi1: fst(t),
exists: x:A. B[x],
pEnvType: pEnvType(T.M[T]),
run-command: run-command(r;t;n),
assert: 
b,
runEvents: runEvents(r),
run-system: run-system(r;t),
run-intransit: run-intransit(r;t),
is-run-event: is-run-event(r;t;x),
outl: outl(x),
isl: isl(x),
band: p 
q,
or: P 
Q,
run-event-loc: run-event-loc(e),
run-event-step: run-event-step(e),
intransit-to-info: intransit-to-info(n2m;l2m;r;env;t;lbl),
run-info: run-info(r;e),
command-to-msg: command-to-msg(c;nmsg;lmsg),
guard: {T},
sq_type: SQType(T),
uall: [x:A]. B[x],
unit: Unit,
bool: 
,
pInTransit: pInTransit(P.M[P]),
lg-is-source: lg-is-source(g;i),
decidable: Dec(P),
System: System(P.M[P]),
InitialSystem: InitialSystem(P.M[P]),
eq_atom: x =a y,
it: 
Lemmas :
lg-size_wf_dag,
pi2_wf,
pInTransit_wf,
ldag_wf,
top_wf,
unit_wf,
pMsg_wf,
Id_wf,
nat_properties,
int_subtype_base,
subtype_base_sq,
le_wf,
pRunType_wf,
nat_wf,
run-command-node_wf,
squash_wf,
run-command_wf,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
bnot_wf,
not_wf,
assert_of_eq_int,
eqtt_to_assert,
assert_wf,
uiff_transitivity,
iff_weakening_uiff,
bool_wf,
eq_int_wf,
lg-is-source_wf_dag,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
assert_of_lt_int,
bool_subtype_base,
bool_cases,
bfalse_wf,
assert_elim,
btrue_neq_bfalse,
le_int_wf,
lt_int_wf,
lg-label_wf_dag,
assert_witness,
decidable__le,
lg-size_wf,
System_wf,
deliver-msg_wf,
lg-size-remove,
is-dag_wf,
lg-remove_wf_dag,
comm-msg_wf,
lg-size-deliver-msg,
assert_of_eq_atom,
com-kind_wf,
eq_atom_wf,
lg-label-remove,
lg-label-deliver-msg,
component_wf,
pRun_wf,
set_subtype_base,
run-event-loc_wf,
run-event-step-positive,
intransit-to-info_wf,
run-info_wf,
runEvents_wf,
subtype_rel_self,
int_seg_wf,
subtype_rel_function,
pi1_wf_top,
decidable__lt,
l_member_wf,
pCom_wf,
false_wf,
true_wf,
member_wf,
fulpRunType_wf,
subtype_rel_simple_product,
InitialSystem_wf,
pEnvType_wf,
strong-type-continuous_wf,
run-event-step_wf,
nat_plus_wf,
is-run-event_wf,
eq_id_self,
uiff_inversion,
nil_member,
or_functionality_wrt_iff,
cons_member,
iff_transitivity,
atom_subtype_base,
run-intransit_wf,
command-to-msg_wf
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}S0:InitialSystem(P.M[P]). \mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]). \mforall{}env:pEnvType(P.M[P]).
let r = pRun(S0;env;n2m;l2m) in
reliable-env(env; r)
{}\mRightarrow{} (\mforall{}tn:run-msg-commands(r)
\mexists{}e:runEvents(r)
let t,n = tn
in (run-info(r;e)
= intransit-to-info(n2m;l2m;r;env;run-event-step(e);run-command(r;t;n)))
\mwedge{} (run-event-loc(e) = (fst(snd(run-command(r;t;n))))))
supposing Continuous+(P.M[P])
Date html generated:
2011_08_17-PM-03_45_31
Last ObjectModification:
2011_06_18-AM-11_26_01
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