Nuprl Lemma : member-eclass-iff-non-empty
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. (↑e ∈b X ⇐⇒ ¬((X es e) = {} ∈ bag(T)))
Proof
Definitions occuring in Statement :
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
apply: f a,
universe: Type,
equal: s = t ∈ T,
empty-bag: {},
bag: bag(T)
Lemmas :
bag_wf,
member-eclass-iff-size,
assert_wf,
member-eclass_wf,
iff_wf,
less_than_wf,
bag-size_wf,
nat_wf,
not_wf,
equal-wf-T-base,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
decidable__le,
equal-wf-base,
empty-bag_wf,
bag-size-zero,
length_of_nil_lemma,
le-add-cancel,
add_functionality_wrt_le,
zero-add,
add-commutes,
add-zero,
minus-zero,
minus-add,
condition-implies-le,
not-le-2,
false_wf,
decidable__lt,
bag_size_empty_lemma
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mneg{}((X es e) = \{\}))
Date html generated:
2015_07_17-PM-00_16_43
Last ObjectModification:
2015_07_16-AM-09_44_34
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