Nuprl Lemma : hdf-until-ap
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:hdataflow(A;C)]. ∀[a:A].
(hdf-until(X;Y)(a)
= <if bag-null(snd(Y(a))) then hdf-until(fst(X(a));fst(Y(a))) else hdf-halt() fi , snd(X(a))>
∈ (hdataflow(A;B) × bag(B)))
Proof
Definitions occuring in Statement :
hdf-until: hdf-until(X;Y),
hdf-halt: hdf-halt(),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
pair: <a, b>,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
bag-null: bag-null(bs),
bag: bag(T)
Lemmas :
hdf-halted_wf,
eqtt_to_assert,
hdf_ap_halt_lemma,
assert-bag-null,
hdataflow-ext,
bag_wf,
unit_wf2,
hdf_halted_inl_red_lemma,
false_wf,
hdf_halted_halt_red_lemma,
hdataflow_wf,
hdf-ap-inl,
hdf-halt_wf,
empty-bag_wf,
equal-wf-T-base,
hdf-ap_wf,
hdf-run_wf,
equal-wf-base,
true_wf,
eqff_to_assert,
equal_wf,
bool_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
hdf-ap-run,
pi2_wf,
squash_wf,
iff_weakening_equal,
bag_null_empty_lemma,
hdf-until_wf,
bag-null_wf,
not_wf
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:hdataflow(A;C)]. \mforall{}[a:A].
(hdf-until(X;Y)(a)
= <if bag-null(snd(Y(a))) then hdf-until(fst(X(a));fst(Y(a))) else hdf-halt() fi , snd(X(a))>)
Date html generated:
2015_07_17-AM-08_06_08
Last ObjectModification:
2015_02_03-PM-09_47_22
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