{ 
[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)
(run-event-state(r;e)
= rev(map(
P.(fst(Process-apply(P;run-event-msg(r;e))));
run-event-state-when(r;e))))
supposing Continuous+(P.M[P]) }
{ Proof }
Definitions occuring in Statement :
run-event-state-when: run-event-state-when(r;e),
run-event-state: run-event-state(r;e),
run-event-msg: run-event-msg(r;e),
runEvents: runEvents(r),
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
System: System(P.M[P]),
Process-apply: Process-apply(P;m),
pMsg: pMsg(P.M[P]),
Process: Process(P.M[P]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
reverse: rev(as),
map: map(f;as),
nat: ,
let: let,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
all: x:A. B[x],
lambda: x.A[x],
function: x:A B[x],
list: type List,
universe: Type,
equal: s = t
Definitions :
prop: 
,
bfalse: ff,
btrue: tt,
all: x:A. B[x],
so_lambda: 
x.t[x],
member: t 
T,
ifthenelse: if b then t else f fi ,
implies: P 
Q,
pi1: fst(t),
pi2: snd(t),
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
so_apply: x[s],
squash: 
T,
cand: A c
B,
true: True,
isl: isl(x),
outl: outl(x),
subtype: S 
T,
top: Top,
false: False,
and: P Q,
le: A 
B,
lelt: i j < k,
int_seg: {i..j
},
exists: 
x:A. B[x],
let: let,
spreadn: spread3,
assert: 
b,
not: 
A,
System: System(P.M[P]),
list_accum: list_accum(x,a.f[x; a];y;l),
reduce: reduce(f;k;as),
ycomb: Y,
filter: filter(P;l),
map: map(f;as),
append: as @ bs,
reverse: rev(as),
deliver-msg: deliver-msg(t;m;x;Cs;L),
mapfilter: mapfilter(f;P;L),
deliver-msg-to-comp: deliver-msg-to-comp(t;m;x;S;C),
iff: P 
Q,
rev_implies: P Q,
component: component(P.M[P]),
nat: ,
compose: f o g,
bool: 
,
uimplies: b supposing a,
uall: [x:A]. B[x],
unit: Unit,
guard: {T},
sq_type: SQType(T),
or: P 
Q,
lg-is-source: lg-is-source(g;i),
pInTransit: pInTransit(P.M[P]),
fulpRunType: fulpRunType(T.M[T]),
it: 
Lemmas :
assert_of_bnot,
eqff_to_assert,
bnot_wf,
uiff_transitivity,
not_wf,
eqtt_to_assert,
assert_wf,
iff_weakening_uiff,
bool_wf,
pInTransit_wf,
lg-is-source_wf_dag,
System_wf,
unit_wf,
pMsg_wf,
Id_wf,
pRun_wf,
true_wf,
ldag_wf,
squash_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
assert_of_lt_int,
bool_subtype_base,
subtype_base_sq,
bool_cases,
top_wf,
strong-type-continuous_wf,
isl_wf,
outl_wf,
member_wf,
bfalse_wf,
assert_elim,
btrue_neq_bfalse,
le_int_wf,
lt_int_wf,
comm-create_wf,
create-component_wf,
it_wf,
not_functionality_wrt_uiff,
comm-msg_wf,
deliver-msg_wf,
component_wf,
lg-remove_wf_dag,
pi2_wf,
pi1_wf_top,
assert_of_eq_atom,
com-kind_wf,
eq_atom_wf,
nat_wf,
lg-size_wf_dag,
le_wf,
lg-label_wf_dag,
eq_id_wf,
reverse_wf,
filter_wf,
map_wf,
append-nil,
Process_wf,
mapfilter_wf,
reverse-reverse,
mapfilter-reverse,
assert-eq-id,
append_wf,
add-cause_wf,
lg-append_wf_dag,
pExt_wf,
Process-apply_wf,
mapfilter-singleton,
mapfilter-append,
l_member_wf,
append_assoc_sq,
subtype_rel_list,
map-map
\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)
(run-event-state(r;e)
= rev(map(\mlambda{}P.(fst(Process-apply(P;run-event-msg(r;e))));run-event-state-when(r;e))))
supposing Continuous+(P.M[P])
Date html generated:
2011_08_16-PM-07_01_44
Last ObjectModification:
2011_06_18-AM-11_15_45
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