Nuprl Lemma : hdf-compose2-ap
∀[A,B,C:Type]. ∀[X:hdataflow(A;B ─→ bag(C))]. ∀[Y:hdataflow(A;B)].
∀[a:A]. (X o Y(a) = <(fst(X(a))) o (fst(Y(a))), ∪f∈snd(X(a)).∪b∈snd(Y(a)).f b> ∈ (hdataflow(A;C) × bag(C)))
supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-compose2: X o Y,
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
bag-combine: ∪x∈bs.f[x],
bag: bag(T)
Lemmas :
hdf-halted_wf,
bool_wf,
eqtt_to_assert,
hdf_ap_halt_lemma,
hdataflow-ext,
bag_wf,
unit_wf2,
hdf_halted_inl_red_lemma,
false_wf,
hdf_halted_halt_red_lemma,
bag_combine_empty_lemma,
hdataflow_wf,
hdf-ap-inl,
hdf-halt_wf,
empty-bag_wf,
true_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bag-combine-empty-right,
not_wf,
hdf-ap-run,
valueall-type-has-valueall,
bag-valueall-type,
bag-combine_wf,
evalall-reduce,
hdf-compose2_wf,
valueall-type_wf
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B {}\mrightarrow{} bag(C))]. \mforall{}[Y:hdataflow(A;B)].
\mforall{}[a:A]. (X o Y(a) = <(fst(X(a))) o (fst(Y(a))), \mcup{}f\mmember{}snd(X(a)).\mcup{}b\mmember{}snd(Y(a)).f b>)
supposing valueall-type(C)
Date html generated:
2015_07_17-AM-08_05_28
Last ObjectModification:
2015_01_27-PM-00_16_58
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