Nuprl Lemma : hdf-once-transformation1
∀[L,G,S,init:Base]. ∀[m:ℕ].
(hdf-once(fix((λmk-hdf,s. (inl (λa.cbva_seq(L[s;a]; λg.<mk-hdf S[g;s], G[g]>; m))))) init)
~ fix((λmk-hdf,s. (inl (λa.cbva_seq(L[s;a]; λg.<case null(G[g]) of inl() => mk-hdf S[g;s] | inr() => inr Ax , G[g]>;
m)))))
init)
Proof
Definitions occuring in Statement :
hdf-once: hdf-once(X),
null: null(as),
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
inr: inr x ,
inl: inl x,
base: Base,
sqequal: s ~ t,
axiom: Ax,
cbva_seq: cbva_seq(L; F; m)
Lemmas :
lifting-strict-decide,
top_wf,
has-value_wf_base,
base_wf,
lifting-strict-spread,
strict4-spread,
cbva_seq-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__le,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
cbva_seq-sqequal-n,
set_subtype_base,
int_subtype_base,
less-iff-le,
minus-zero,
minus-minus,
le-add-cancel-alt,
le-add-cancel2,
add-mul-special,
zero-mul,
lelt_wf,
subtype_base_sq,
not-equal-2,
nat_wf,
all_wf,
sqequal_n_wf,
int_seg_subtype-nat,
set_wf,
less_than_wf,
primrec-wf2,
sq_stable__le
\mforall{}[L,G,S,init:Base]. \mforall{}[m:\mBbbN{}].
(hdf-once(fix((\mlambda{}mk-hdf,s. (inl (\mlambda{}a.cbva\_seq(L[s;a]; \mlambda{}g.<mk-hdf S[g;s], G[g]> m))))) init)
\msim{} fix((\mlambda{}mk-hdf,s. (inl (\mlambda{}a.cbva\_seq(L[s;a]; \mlambda{}g.<case null(G[g])
of inl() =>
mk-hdf S[g;s]
| inr() =>
inr Ax
, G[g]
> m)))))
init)
Date html generated:
2015_07_17-AM-08_15_22
Last ObjectModification:
2015_01_27-AM-11_51_55
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