Nuprl Lemma : hdf-sqequal1
∀[F:Top]. (hdf-base(m.F[m]) ~ fix((λmk-hdf.(inl (λm.<mk-hdf, F[m]>)))))
Proof
Definitions occuring in Statement :
hdf-base: hdf-base(m.F[m]),
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
Lemmas :
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-cancel2,
add-mul-special,
zero-mul,
le-add-cancel-alt,
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:Top]. (hdf-base(m.F[m]) \msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}m.<mk-hdf, F[m]>)))))
Date html generated:
2015_07_17-AM-08_08_09
Last ObjectModification:
2015_01_27-PM-00_06_34
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