Nuprl Lemma : hdf-union-ap
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:hdataflow(A;C)]. ∀[a:A].
(X + Y(a)
= <fst(X(a)) + fst(Y(a)), bag-map(λx.(inl x);snd(X(a))) + bag-map(λx.(inr x );snd(Y(a)))>
∈ (hdataflow(A;B + C) × bag(B + C))) supposing
(valueall-type(B) and
valueall-type(C))
Proof
Definitions occuring in Statement :
hdf-union: X + 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),
lambda: λx.A[x],
pair: <a, b>,
product: x:A × B[x],
inr: inr x ,
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T,
bag-append: as + bs,
bag-map: bag-map(f;bs),
bag: bag(T)
Lemmas :
valueall-type_wf,
hdataflow_wf,
unit_wf2,
true_wf,
false_wf,
not_wf,
hdf-ap-run,
hdf-ap-inl,
hdf_halted_inl_red_lemma,
bag_wf,
hdataflow-ext,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
hdf_halted_halt_red_lemma,
empty_bag_append_lemma,
bag_map_empty_lemma,
hdf_ap_halt_lemma,
hdf-halted-is-halt,
eqtt_to_assert,
bool_wf,
hdf-halted_wf,
empty-bag_wf,
hdf-halt_wf,
hdf-run_wf,
evalall-reduce,
bag-map_wf,
void-valueall-type,
union-valueall-type,
bag-valueall-type,
valueall-type-has-valueall,
hdf-ap_wf,
hdf-union_wf,
bag-append_wf,
mk-hdf_wf,
subtype_rel_wf,
subtype_rel_simple_product,
subtype_rel_function,
subtype_rel_sum,
subtype-corec1,
it_wf,
assert_wf,
assert_of_band
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:hdataflow(A;C)]. \mforall{}[a:A].
(X + Y(a)
= <fst(X(a)) + fst(Y(a))
, bag-map(\mlambda{}x.(inl x);snd(X(a))) + bag-map(\mlambda{}x.(inr x );snd(Y(a)))
>) supposing
(valueall-type(B) and
valueall-type(C))
Date html generated:
2015_07_17-AM-08_06_39
Last ObjectModification:
2015_01_29-PM-04_32_10
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