Nuprl Lemma : parallel-compose2-program-eq
∀[Info,B,C:Type]. ∀[X1,X2:Id ─→ hdataflow(Info;B ─→ bag(C))]. ∀[X:Id ─→ hdataflow(Info;B)].
(X1 o X || X2 o X = X1 || X2 o X ∈ (Id ─→ hdataflow(Info;C))) supposing
(valueall-type(C) and
valueall-type(B) and
(↓B))
Proof
Definitions occuring in Statement :
parallel-class-program: X || Y,
eclass2-program: Xpr o Ypr,
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
squash: ↓T,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T),
hdataflow: hdataflow(A;B)
Lemmas :
bag-value-type,
local-class-equality,
eclass2_wf,
parallel-class_wf,
bag_wf,
hdataflow-class_wf,
parallel-class-program_wf,
eclass2-program_wf,
pi2_wf,
hdataflow_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
es-loc_wf,
event-ordering+_subtype,
map_wf,
es-E_wf,
es-info_wf,
es-before_wf,
event-ordering+_wf,
all_wf,
equal_wf,
class-ap_wf,
sq_exists_subtype_rel,
Id_wf,
iff_weakening_equal,
squash_wf,
true_wf,
eclass_wf,
parallel-eclass2-left,
function-valueall-type,
list_wf,
valueall-type_wf,
bool_wf,
hdf-compose2_wf,
hdf-parallel_wf,
hdf-halted_wf,
eqtt_to_assert,
bor_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
iff_imp_equal_bool,
btrue_wf,
assert_wf,
or_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
assert_of_bor,
iff_wf,
hdf-parallel-halted,
band_wf,
hdf-halted-compose2-iterate
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X1,X2:Id {}\mrightarrow{} hdataflow(Info;B {}\mrightarrow{} bag(C))]. \mforall{}[X:Id {}\mrightarrow{} hdataflow(Info;B)].
(X1 o X || X2 o X = X1 || X2 o X) supposing (valueall-type(C) and valueall-type(B) and (\mdownarrow{}B))
Date html generated:
2015_07_22-PM-00_03_53
Last ObjectModification:
2015_02_04-PM-05_10_30
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