Nuprl Lemma : hdf-base-transformation2
∀[F:Top]. (hdf-base(m.F[m]) ~ fix((λmk-hdf,s. (inl (λa.cbva_seq(λx.⊥; λg.<mk-hdf Ax, F[a]>; 0))))) Ax)
Proof
Definitions occuring in Statement :
hdf-base: hdf-base(m.F[m]),
bottom: ⊥,
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,
axiom: Ax,
cbva_seq: cbva_seq(L; F; m)
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
fun_exp0_lemma,
strictness-apply,
bottom_diverge,
has-value_wf_base,
decidable__le,
subtract_wf,
false_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,
top_wf
\mforall{}[F:Top]. (hdf-base(m.F[m]) \msim{} fix((\mlambda{}mk-hdf,s. (inl (\mlambda{}a.cbva\_seq(\mlambda{}x.\mbot{}; \mlambda{}g.<mk-hdf Ax, F[a]> 0))))) A\000Cx)
Date html generated:
2015_07_17-AM-08_08_22
Last ObjectModification:
2015_01_27-PM-00_06_03
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