Nuprl Lemma : parallel-bag-classrel
∀[B,Info,T:Type]. ∀[X:T ─→ EClass(B)]. ∀[as:bag(T)]. ∀[v:B]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(v ∈ (||a∈as.X[a])(e);↓∃a:T. (a ↓∈ as ∧ v ∈ X[a](e)))
Proof
Definitions occuring in Statement :
parallel-bag-class: (||a∈as.X[a]),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
so_apply: x[s],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
iff_weakening_uiff,
classrel_wf,
bind-class_wf,
return-loc-bag-class_wf,
Id_wf,
squash_wf,
exists_wf,
es-le_wf,
eo-forward_wf,
member-eo-forward-E,
equal_wf,
es-loc_wf,
bind-class-rel,
bag-member_wf,
uiff_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
bag_wf,
eclass_wf,
true_wf,
eo-forward-trivial,
iff_weakening_equal,
assert_wf,
es-first_wf2,
return-loc-bag-class-classrel,
es-init-le,
es-first-init,
es-init_wf
Latex:
\mforall{}[B,Info,T:Type]. \mforall{}[X:T {}\mrightarrow{} EClass(B)]. \mforall{}[as:bag(T)]. \mforall{}[v:B]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(v \mmember{} (||a\mmember{}as.X[a])(e);\mdownarrow{}\mexists{}a:T. (a \mdownarrow{}\mmember{} as \mwedge{} v \mmember{} X[a](e)))
Date html generated:
2015_07_22-PM-00_06_27
Last ObjectModification:
2015_02_04-PM-04_42_13
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