Nuprl Lemma : hdf-state-base
∀[f,C,F,s:Top].
(hdf-state((λx,s. f[x;s]) o hdf-base(a.if C[a] then [F[a]] else [] fi );[s])
~ fix((λmk-hdf,s. (inl (λa.cbva_seq(λn.if C[a] then f[F[a];s] else s fi ; λg.<mk-hdf (g (λx.x)), g (λx.[x])>; 1))))) s\000C)
Proof
Definitions occuring in Statement :
hdf-state: hdf-state(X;bs),
hdf-compose1: f o X,
hdf-base: hdf-base(m.F[m]),
cons: [a / b],
nil: [],
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
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,
cbva_seq: cbva_seq(L; F; m)
Lemmas :
hdf-base-transformation1,
hdf-compose1-transformation1-2,
false_wf,
le_wf,
hdf-state-transformation2,
primrec0_lemma,
primrec1_lemma,
map-ifthenelse,
map_cons_lemma,
map_nil_lemma,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
base_wf,
fun_exp0_lemma,
strictness-apply,
bottom-sqle,
decidable__le,
subtract_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
fun_exp_unroll_1,
bag-combine-unit-left-top,
list_ind_cons_lemma,
list_ind_nil_lemma,
callbyvalueall-single,
cbv_sqle,
int_subtype_base,
evalall-sqequal,
null_cons_lemma,
has-valueall-single,
has-value_wf_base,
has-valueall_wf_base,
top_wf,
primrec-unroll,
callbyvalueall-ifthenelse
\mforall{}[f,C,F,s:Top].
(hdf-state((\mlambda{}x,s. f[x;s]) o hdf-base(a.if C[a] then [F[a]] else [] fi );[s])
\msim{} fix((\mlambda{}mk-hdf,s. (inl (\mlambda{}a.cbva\_seq(\mlambda{}n.if C[a] then f[F[a];s] else s fi ; \mlambda{}g.<mk-hdf (g (\mlambda{}x.x))
, g (\mlambda{}x.[x])
> 1)))))
s)
Date html generated:
2015_07_17-AM-08_15_31
Last ObjectModification:
2015_04_23-PM-11_31_52
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