Nuprl Lemma : hdf-once-transformation2
∀[L,G,S,init:Top]. ∀[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],
top: Top,
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,
sqequal: s ~ t,
axiom: Ax,
cbva_seq: cbva_seq(L; F; m)
Lemmas :
lifting-strict-decide,
has-value_wf_base,
base_wf,
is-exception_wf,
top_wf,
lifting-strict-spread,
strict4-spread,
cbva_seq-spread,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
nat_wf,
strictness-apply,
lifting-strict-ispair,
lifting-strict-isaxiom,
lifting-strict-less,
strictness-decide,
bottom-sqle,
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,
le_weakening2,
le_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
le_weakening,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
bottom_diverge,
exception-not-bottom,
subtract-elim
\mforall{}[L,G,S,init:Top]. \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_26
Last ObjectModification:
2015_06_19-PM-00_53_22
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