Nuprl Lemma : iterate-hdf-buffer2-simple
∀[A,B:Type]. ∀[X:hdataflow(A;B ─→ B)]. ∀[bs:bag(B)].
∀[L:A List]. ∀[a:A]. ((snd(hdf-buffer2(X;bs)*(L)(a))) = (snd(simple-hdf-buffer2(X;bs)*(L)(a))) ∈ bag(B))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-buffer2: hdf-buffer2(X;bs),
simple-hdf-buffer2: simple-hdf-buffer2(X;bs),
iterate-hdataflow: P*(inputs),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi2: snd(t),
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
bag_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
hdataflow-ext,
unit_wf2,
iter_hdf_nil_lemma,
empty-bag_wf,
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,
iter_hdf_cons_lemma,
iterate-hdf-halt,
subtype_rel_list,
top_wf,
list_wf,
valueall-type_wf,
hdataflow_wf,
valueall-type-has-valueall,
bag-valueall-type,
bag-combine_wf,
bag-map_wf,
bag-null_wf,
bool_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
assert-bag-null,
evalall-reduce
\mforall{}[A,B:Type]. \mforall{}[X:hdataflow(A;B {}\mrightarrow{} B)]. \mforall{}[bs:bag(B)].
\mforall{}[L:A List]. \mforall{}[a:A]. ((snd(hdf-buffer2(X;bs)*(L)(a))) = (snd(simple-hdf-buffer2(X;bs)*(L)(a))))
supposing valueall-type(B)
Date html generated:
2015_07_17-AM-08_07_57
Last ObjectModification:
2015_01_27-PM-00_08_17
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