Nuprl Lemma : datastream-dataflow-to-Process
∀[A,B:Type]. ∀[g:B ─→ LabeledDAG(Id × (Com(P.A) Process(P.A)))]. ∀[L:A List]. ∀[F:dataflow(A;B)].
(data-stream(dataflow-to-Process(
F;
g);L) ~ map(g;data-stream(F;L)))
Proof
Definitions occuring in Statement :
dataflow-to-Process: dataflow-to-Process,
Process: Process(P.M[P]),
Com: Com(P.M[P]),
data-stream: data-stream(P;L),
dataflow: dataflow(A;B),
ldag: LabeledDAG(T),
Id: Id,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
sqequal: s ~ t
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
dataflow_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
data_stream_nil_lemma,
map_nil_lemma,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
list_wf,
ldag_wf,
Id_wf,
Com_wf,
Process_wf,
subtype_rel_list,
top_wf,
rec_dataflow_ap_lemma,
map_cons_lemma,
dataflow-ap_wf,
data-stream-cons
Latex:
\mforall{}[A,B:Type]. \mforall{}[g:B {}\mrightarrow{} LabeledDAG(Id \mtimes{} (Com(P.A) Process(P.A)))]. \mforall{}[L:A List]. \mforall{}[F:dataflow(A;B)].
(data-stream(dataflow-to-Process(
F;
g);L) \msim{} map(g;data-stream(F;L)))
Date html generated:
2015_07_23-AM-11_07_39
Last ObjectModification:
2015_01_29-AM-00_10_10
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