Nuprl Lemma : hdf-compose1-transformation0-2
∀[f,F:Top].
(f o fix((λmk-hdf.(inl (λa.<mk-hdf, F[a]>)))) ~ fix((λmk-hdf.(inl (λa.cbva_seq(λn.bag-map(f;F[a]); λg.<mk-hdf
, g (λx.x)
>; 1))))))
Proof
Definitions occuring in Statement :
hdf-compose1: f o X,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
natural_number: $n,
sqequal: s ~ t,
bag-map: bag-map(f;bs),
cbva_seq: cbva_seq(L; F; m)
Lemmas :
lifting-strict-decide,
top_wf,
has-value_wf_base,
base_wf,
lifting-strict-spread,
strict4-spread,
lifting-strict-callbyvalueall,
lifting-strict-callbyvalue,
has-valueall-if-has-value-callbyvalueall,
has-valueall-has-value,
lifting-strict-ispair,
lifting-strict-isaxiom,
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,
all_wf,
sqequal_n_wf,
int_seg_subtype-nat,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
lelt_wf,
set_wf,
less_than_wf,
primrec-wf2,
nat_wf,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
minus-zero,
le-add-cancel2,
subtype_base_sq,
int_subtype_base,
set_subtype_base
\mforall{}[f,F:Top].
(f o fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.<mk-hdf, F[a]>)))) \msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.cbva\_seq(\mlambda{}n.bag-map(f;F[a]);
\mlambda{}g.<mk-hdf
, g (\mlambda{}x.x)
> 1))))))
Date html generated:
2015_07_17-AM-08_08_32
Last ObjectModification:
2015_01_29-PM-06_31_32
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