Nuprl Lemma : assert-member-eclass
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. (↑e ∈b X ⇐⇒ ↓∃v:T. v ∈ X(e))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
squash: ↓T,
universe: Type
Lemmas :
bag_wf,
assert_wf,
bnot_wf,
eq_int_wf,
bag-size_wf,
nat_wf,
not_wf,
equal-wf-T-base,
iff_wf,
squash_wf,
exists_wf,
bag-member_wf,
member-eclass_wf,
classrel_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert_of_eq_int,
bag-member-iff-size,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}v:T. v \mmember{} X(e))
Date html generated:
2015_07_17-PM-00_16_29
Last ObjectModification:
2015_01_28-AM-00_03_48
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