Nuprl Lemma : global-class-iff-bounded-local-class
∀[Info:Type]. ∀[A:{A:Type| valueall-type(A)} ]. ∀[X:EClass(A)].
(GlobalClass(Info;A;X) ⇐⇒ LocalClass(X) ∧ LocBounded(A;X))
Proof
Definitions occuring in Statement :
global-class: GlobalClass(Info;A;X),
local-class: LocalClass(X),
loc-bounded-class: LocBounded(T;X),
eclass: EClass(A[eo; e]),
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
universe: Type
Lemmas :
global-class_wf,
local-class_wf,
loc-bounded-class_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
valueall-type_wf,
hdf-parallel-bag_wf,
bag-mapfilter_wf,
Id_wf,
hdataflow_wf,
eq_id_wf,
assert_wf,
sq_stable__valueall-type,
bag_wf,
class-ap_wf,
squash_wf,
true_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
es-loc_wf,
map_wf,
es-info_wf,
es-before_wf,
iff_weakening_equal,
all_wf,
equal_wf,
bag-union_wf,
pi2_wf,
hdf-parallel-bag-iterate,
bag_all_wf,
hdf-halted_wf,
bag-map_wf,
bool_wf,
eqtt_to_assert,
hdf_ap_halt_lemma,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bag-map-mapfilter,
assert-bag_all,
assert-bag-null,
bag-null-bag-union,
bag-member-map,
bag-filter_wf,
bag-member-filter-set,
assert-eq-id,
and_wf,
bag-member_wf,
hdf-halted-is-halt,
hdf-ap-run,
bag-map-map,
value-type-has-value,
bag-value-type,
valueall-type-has-valueall,
bag-valueall-type,
bag-combine_wf,
evalall-reduce,
bag-combine-mapfilter,
top_wf,
empty-bag_wf,
bag-combine-filter,
classrel_wf,
bag-member-union,
class-loc-bound_wf,
sq_stable__all,
sq_stable__equal,
bag-remove-repeats_wf,
id-deq_wf,
bag-mapfilter-map,
decidable__bag-member2,
decidable__equal_Id,
bag-extensionality2,
single-bag_wf,
subtype_rel_bag,
bag-member-single,
bag-count-filter,
count-bag-remove-repeats,
bag-member-filter,
lt_int_wf,
bag-count_wf,
nat_wf,
bag-count-single,
subtype_rel-deq,
set_wf,
bag-member-remove-repeats,
bag-member-count,
le_antisymmetry,
deq_wf,
bnot_wf,
not_wf,
less_than_wf,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
bool_cases,
assert_of_lt_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
bag_map_single_lemma,
bag-union-single,
bag-subtype-list,
null-bag-mapfilter,
bag-null-filter,
bag_union_empty_lemma,
decidable__assert,
bag-null_wf,
bag-member-not-bag-null,
sq_stable__bag-member
\mforall{}[Info:Type]. \mforall{}[A:\{A:Type| valueall-type(A)\} ]. \mforall{}[X:EClass(A)].
(GlobalClass(Info;A;X) \mLeftarrow{}{}\mRightarrow{} LocalClass(X) \mwedge{} LocBounded(A;X))
Date html generated:
2015_07_17-PM-00_34_29
Last ObjectModification:
2015_02_04-PM-05_33_22
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