Nuprl Lemma : hdf-sqequal4
∀[F1,F2:Top].
(fix((λmk-hdf.(inl (λa.let out ←─ F1[a]
in <mk-hdf, out>)))) || fix((λmk-hdf.(inl (λa.let out ←─ F2[a]
in <mk-hdf, out>))))
~ fix((λmk-hdf.(inl (λa.let out1 ←─ F1[a]
in let out2 ←─ F2[a]
in let out ←─ out1 + out2
in <mk-hdf, out>)))))
Proof
Definitions occuring in Statement :
hdf-parallel: X || Y,
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
sqequal: s ~ t,
bag-append: as + bs
Lemmas :
lifting-strict-spread,
top_wf,
has-value_wf_base,
base_wf,
lifting-strict-decide,
strict4-spread,
lifting-strict-callbyvalueall,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
decidable__lt,
decidable__le,
not-le-2,
less-iff-le,
condition-implies-le,
add-associates,
minus-add,
minus-zero,
add-zero,
add-commutes,
add-swap,
minus-minus,
minus-one-mul,
zero-add,
add_functionality_wrt_le,
le-add-cancel-alt,
le-add-cancel2,
add-mul-special,
zero-mul,
lelt_wf,
subtype_base_sq,
int_subtype_base,
not-equal-2,
le-add-cancel,
nat_wf,
set_subtype_base,
all_wf,
sqequal_n_wf,
int_seg_subtype-nat,
set_wf,
less_than_wf,
primrec-wf2,
sq_stable__le
\mforall{}[F1,F2:Top].
(fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out \mleftarrow{}{} F1[a]
in <mk-hdf, out>)))) || fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out \mleftarrow{}{} F2[a]
in <mk-hdf, out>))))
\msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out1 \mleftarrow{}{} F1[a]
in let out2 \mleftarrow{}{} F2[a]
in let out \mleftarrow{}{} out1 + out2
in <mk-hdf, out>)))))
Date html generated:
2015_07_17-AM-08_17_01
Last ObjectModification:
2015_01_27-AM-11_51_50
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