Nuprl Lemma : member-class-at
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[locs:bag(Id)]. uiff(↑e ∈b X@locs;(↑e ∈b X) ∧ loc(e) ↓∈ locs)
Proof
Definitions occuring in Statement :
class-at: X@locs,
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
assert_witness,
assert_wf,
member-eclass_wf,
class-at_wf,
bag-member_wf,
es-loc_wf,
Id_wf,
event-ordering+_subtype,
bag_wf,
es-E_wf,
event-ordering+_wf,
eclass_wf,
member-eclass-iff-size,
less_than_wf,
bag-size_wf,
nat_wf,
bag-deq-member_wf,
id-deq_wf,
bnot_wf,
not_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-bag-deq-member,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
equal-wf-T-base,
uiff_transitivity
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[locs:bag(Id)].
uiff(\muparrow{}e \mmember{}\msubb{} X@locs;(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} loc(e) \mdownarrow{}\mmember{} locs)
Date html generated:
2015_07_23-AM-11_27_40
Last ObjectModification:
2015_01_28-PM-11_14_45
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