Nuprl Lemma : hdf-compose1-transformation1
∀[f,L:Base]. ∀[m:ℕ+].
(f o fix((λmk-hdf.(inl (λa.simple-cbva-seq(L[a];λout.<mk-hdf, out>;m)))))
~ fix((λmk-hdf.(inl (λa.simple-cbva-seq(λn.if (n =z m)
then mk_lambdas(λout.bag-map(f;out);m - 1)
else L[a] n
fi ;λout.<mk-hdf, out>;m + 1))))))
Proof
Definitions occuring in Statement :
hdf-compose1: f o X,
nat_plus: ℕ+,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
so_apply: x[s],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
subtract: n - m,
add: n + m,
natural_number: $n,
base: Base,
sqequal: s ~ t,
bag-map: bag-map(f;bs),
simple-cbva-seq: simple-cbva-seq(L;F;m),
mk_lambdas: mk_lambdas(F;m)
Lemmas :
nat_plus_wf,
base_wf,
lifting-strict-decide,
top_wf,
has-value_wf_base,
lifting-strict-spread,
strict4-spread,
lifting-strict-callbyvalueall,
lifting-strict-int_eq,
simple-cbva-seq-spread,
simple-cbva-seq-extend-2,
decidable__lt,
subtract_wf,
subtype_base_sq,
int_subtype_base,
decidable__equal_int,
false_wf,
not-equal-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-commutes,
add-associates,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
minus-zero,
add-swap,
le-add-cancel-alt,
nat_wf,
set_subtype_base,
le_wf,
all_wf,
int_seg_wf,
sqequal_n_wf,
less_than_wf,
int_seg_subtype-nat,
complete_nat_ind,
simple-cbva-seq-sqequal-n,
decidable__le,
not-le-2,
le-add-cancel2,
lelt_wf
\mforall{}[f,L:Base]. \mforall{}[m:\mBbbN{}\msupplus{}].
(f o fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.simple-cbva-seq(L[a];\mlambda{}out.<mk-hdf, out>m)))))
\msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.simple-cbva-seq(\mlambda{}n.if (n =\msubz{} m)
then mk\_lambdas(\mlambda{}out.bag-map(f;out);m - 1)
else L[a] n
fi ;\mlambda{}out.<mk-hdf, out>m + 1))))))
Date html generated:
2015_07_17-AM-08_08_35
Last ObjectModification:
2015_01_27-PM-00_06_28
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