Nuprl Lemma : hdf-once-transformation3
∀[L,G:Top]. ∀[m:ℕ].
(hdf-once(fix((λmk-hdf.(inl (λa.cbva_seq(L[a]; λg.<mk-hdf, G[a;g]>; m))))))
~ fix((λmk-hdf.(inl (λa.cbva_seq(L[a]; λg.<case null(G[a;g]) of inl() => mk-hdf | inr() => inr Ax , G[a;g]>; m))))))
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],
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_1,
bottom_diverge,
exception-not-bottom,
set_subtype_base,
le_wf,
int_subtype_base
\mforall{}[L,G:Top]. \mforall{}[m:\mBbbN{}].
(hdf-once(fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.cbva\_seq(L[a]; \mlambda{}g.<mk-hdf, G[a;g]> m))))))
\msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.cbva\_seq(L[a]; \mlambda{}g.<case null(G[a;g]) of inl() => mk-hdf | inr() => inr Ax
, G[a;g]
> m))))))
Date html generated:
2015_07_17-AM-08_15_28
Last ObjectModification:
2015_06_19-PM-01_00_19
Home
Index