Nuprl Lemma : hdf-union-eq-disju
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:hdataflow(A;C)].
(X + Y = (λx.(inl x)) o X || (λx.(inr x )) o Y ∈ hdataflow(A;B + C)) supposing
(valueall-type(B) and
valueall-type(C))
Proof
Definitions occuring in Statement :
hdf-union: X + Y,
hdf-parallel: X || Y,
hdf-compose1: f o X,
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
inr: inr x ,
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T
Lemmas :
hdataflow-equal,
hdf-union_wf,
hdf-parallel_wf,
hdf-compose1_wf,
union-valueall-type,
list_wf,
valueall-type_wf,
hdataflow_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
iter_hdf_nil_lemma,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
iter_hdf_cons_lemma,
hdf-halted_wf,
bool_wf,
eqtt_to_assert,
hdf_halted_halt_red_lemma,
empty_bag_append_lemma,
btrue_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
hdf_halted_run_red_lemma,
bfalse_wf,
hdf-ap_wf,
bag_wf,
iterate-hdataflow_wf,
iff_weakening_equal,
hdf-parallel-ap,
hdf-compose1-ap,
squash_wf,
true_wf,
pi1_wf_top,
top_wf,
hdf-union-ap,
subtype_rel_product,
subtype_top,
list_induction,
all_wf,
hdf-out_wf,
hdf_out_halt_red_lemma,
hdf-ap-run,
hdataflow-ext,
unit_wf2,
hdf_halted_inl_red_lemma,
bag_map_empty_lemma,
hdf-ap-inl,
valueall-type-has-valueall,
bag-valueall-type,
bag-map_wf,
evalall-reduce,
void-valueall-type,
not_wf,
bag-append_wf,
empty-bag_wf,
hdf-out-run
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:hdataflow(A;C)].
(X + Y = (\mlambda{}x.(inl x)) o X || (\mlambda{}x.(inr x )) o Y) supposing
(valueall-type(B) and
valueall-type(C))
Date html generated:
2015_07_17-AM-08_06_42
Last ObjectModification:
2015_02_03-PM-09_53_03
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