Nuprl Lemma : system-strongly-realizes_functionality
∀[M:Type ─→ Type]
∀n2m:ℕ ─→ pMsg(P.M[P]). ∀l2m:Id ─→ pMsg(P.M[P]).
∀[A:pEnvType(P.M[P]) ─→ pRunType(P.M[P]) ─→ ℙ]. ∀[B:EO+(pMsg(P.M[P])) ─→ ℙ].
∀X,Y:InitialSystem(P.M[P]).
(system-equiv(P.M[P];X;Y) ⇒ assuming(env,r.A[env;r]) X |= eo.B[eo] ⇒ assuming(env,r.A[env;r]) Y |= eo.B[eo])
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
system-strongly-realizes: system-strongly-realizes,
InitialSystem: InitialSystem(P.M[P]),
pEnvType: pEnvType(T.M[T]),
pRunType: pRunType(T.M[T]),
system-equiv: system-equiv(T.M[T];S1;S2),
pMsg: pMsg(P.M[P]),
event-ordering+: EO+(Info),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
decidable__exists_int_seg,
length_wf,
component_wf,
equal_wf,
int_seg_wf,
decidable__equal_int,
map_wf,
decidable_wf,
exists_wf,
select_wf,
zero-le-nat,
int_seg_subtype-nat,
false_wf,
non_neg_length,
length_wf_nat,
sq_stable__le,
upto_wf,
list_wf,
ldag_wf,
pInTransit_wf,
std-initial_wf,
set_wf,
System_wf,
map-length,
length_upto,
and_wf,
lg-contains_wf,
select-map,
subtype_rel_list,
top_wf,
less_than_transitivity1,
le_weakening,
lelt_wf,
subtype_base_sq,
int_subtype_base,
select_upto,
iff_weakening_equal,
Id_wf,
process-equiv_wf,
Process-stream_wf,
pMsg_wf,
subtype_rel_dep_function,
subtype_rel-int_seg,
subtype_rel_self,
squash_wf,
le_wf,
less_than_wf,
increasing_inj,
equal-wf-base-T,
increasing_wf,
all_wf,
system-equiv_wf,
sub-system_wf,
pRun_functionality,
pRunType_wf,
run-eo_wf,
runEvents_wf,
std-initial-property,
run-initialization_wf,
run-initialization-property,
member_wf,
run-info_wf,
subtype_rel_wf,
run-event-step_wf,
nat_wf
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]).
\mforall{}[A:pEnvType(P.M[P]) {}\mrightarrow{} pRunType(P.M[P]) {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:EO+(pMsg(P.M[P])) {}\mrightarrow{} \mBbbP{}].
\mforall{}X,Y:InitialSystem(P.M[P]).
(system-equiv(P.M[P];X;Y)
{}\mRightarrow{} assuming(env,r.A[env;r])
X |= eo.B[eo]
{}\mRightarrow{} assuming(env,r.A[env;r])
Y |= eo.B[eo])
supposing Continuous+(P.M[P])
Date html generated:
2015_07_23-AM-11_20_24
Last ObjectModification:
2015_02_04-PM-04_53_35
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