Nuprl Lemma : hdf-parallel-bag-iterate
∀[A,B:Type]. ∀[Xs:bag(hdataflow(A;B))]. ∀[inputs:A List].
hdf-parallel-bag(Xs)*(inputs) = hdf-parallel-bag(bag-map(λx.x*(inputs);Xs)) ∈ hdataflow(A;B)
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-parallel-bag: hdf-parallel-bag(Xs),
iterate-hdataflow: P*(inputs),
hdataflow: hdataflow(A;B),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T,
bag-map: bag-map(f;bs),
bag: bag(T)
Lemmas :
list_induction,
all_wf,
equal_wf,
iterate-hdataflow_wf,
hdf-parallel-bag_wf,
bag-map_wf,
list_wf,
iter_hdf_nil_lemma,
squash_wf,
valueall-type_wf,
bag-map-trivial,
iff_weakening_equal,
iter_hdf_cons_lemma,
bag_all_wf,
hdf-halted_wf,
bool_wf,
eqtt_to_assert,
hdf_ap_halt_lemma,
iterate-hdf-halt,
subtype_rel_list,
top_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bag_wf,
hdataflow_wf,
bag_all-map,
assert-bag_all,
hdf-halted-is-halt,
hdf_halted_halt_red_lemma,
bag-member_wf,
hdf-halt_wf,
hdf-ap-run,
value-type-has-value,
bag-value-type,
hdf-ap_wf,
valueall-type-has-valueall,
bag-valueall-type,
bag-combine_wf,
evalall-reduce,
bag-map-map
\mforall{}[A,B:Type]. \mforall{}[Xs:bag(hdataflow(A;B))]. \mforall{}[inputs:A List].
hdf-parallel-bag(Xs)*(inputs) = hdf-parallel-bag(bag-map(\mlambda{}x.x*(inputs);Xs))
supposing valueall-type(B)
Date html generated:
2015_07_17-AM-08_06_27
Last ObjectModification:
2015_02_03-PM-09_47_19
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