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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
parallel-bag-class: (||a∈as.X[a]),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
squash: ↓T,
rev_implies: P ⇐ Q,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cand: A c∧ B,
true: True,
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt
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:
2016_05_17-AM-09_13_12
Last ObjectModification:
2016_01_17-PM-11_15_26
Theory : classrel!lemmas
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