Nuprl Lemma : hdf-sqequal2-cbva
∀[F,G,H:Top].
(fix((λmk-hdf,s0. case s0 of inl(y) => inl (λa.let X',bs = y a in let out ←─ G[bs] in <mk-hdf X', out>) | inr(z) => H[\000Cz]))
fix((λmk-hdf.(inl (λm.let out ←─ F[m]
in <mk-hdf, out>)))) ~ fix((λmk-hdf.(inl (λa.let out1 ←─ F[a]
in let out2 ←─ G[out1]
in <mk-hdf, out2>)))))
Proof
Definitions occuring in Statement :
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
spread: spread def,
pair: <a, b>,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
inl: inl x,
sqequal: s ~ t
Lemmas :
lifting-strict-callbyvalueall,
strict4-spread,
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,
base_wf,
all_wf,
sqequal_n_wf,
int_seg_subtype-nat,
set_wf,
less_than_wf,
primrec-wf2,
sq_stable__le,
top_wf
\mforall{}[F,G,H:Top].
(fix((\mlambda{}mk-hdf,s0. case s0
of inl(y) =>
inl (\mlambda{}a.let X',bs = y a
in let out \mleftarrow{}{} G[bs]
in <mk-hdf X', out>)
| inr(z) =>
H[z]))
fix((\mlambda{}mk-hdf.(inl (\mlambda{}m.let out \mleftarrow{}{} F[m]
in <mk-hdf, out>)))) \msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out1 \mleftarrow{}{} F[a]
in let out2 \mleftarrow{}{} G[out1]
in <mk-hdf, out2>)))))
Date html generated:
2015_07_17-AM-08_08_12
Last ObjectModification:
2015_01_27-PM-00_06_25
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