Nuprl Lemma : hdf-parallel-ap
∀[A,B:Type]. ∀[X,Y:hdataflow(A;B)]. ∀[a:A].
X || Y(a) = <fst(X(a)) || fst(Y(a)), (snd(X(a))) + (snd(Y(a)))> ∈ (hdataflow(A;B) × bag(B)) supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-parallel: X || Y,
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
pair: <a, b>,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
bag-append: as + bs,
bag: bag(T)
Lemmas :
hdf-halted_wf,
bool_wf,
eqtt_to_assert,
hdf_ap_halt_lemma,
hdataflow-ext,
bag_wf,
unit_wf2,
hdf_halted_inl_red_lemma,
false_wf,
hdf_halted_halt_red_lemma,
empty_bag_append_lemma,
hdf-halt_wf,
empty-bag_wf,
true_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
hdf-ap-run,
hdf-ap-inl,
valueall-type-has-valueall,
bag-valueall-type,
evalall-reduce,
hdf-parallel_wf,
not_wf,
bag-append_wf,
valueall-type_wf,
hdataflow_wf
\mforall{}[A,B:Type]. \mforall{}[X,Y:hdataflow(A;B)]. \mforall{}[a:A].
X || Y(a) = <fst(X(a)) || fst(Y(a)), (snd(X(a))) + (snd(Y(a)))> supposing valueall-type(B)
Date html generated:
2015_07_17-AM-08_06_22
Last ObjectModification:
2015_01_27-PM-00_17_05
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