Nuprl Lemma : member-eclass-iff-size
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. (↑e ∈b X ⇐⇒ 0 < #(X es e))
Proof
Definitions occuring in Statement :
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
less_than: a < b,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
apply: f a,
natural_number: $n,
universe: Type,
bag-size: #(bs)
Lemmas :
assert_wf,
bnot_wf,
eq_int_wf,
bag-size_wf,
nat_wf,
iff_transitivity,
not_wf,
equal-wf-T-base,
iff_weakening_uiff,
assert_of_bnot,
assert_of_eq_int,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
less_than_wf,
member-less_than,
assert_witness,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} 0 < \#(X es e))
Date html generated:
2015_07_17-PM-00_16_35
Last ObjectModification:
2015_01_28-AM-00_01_42
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