Nuprl Lemma : member-class-output
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[bg:bag(E)]. ∀[v:T].
uiff(v ↓∈ class-output(X;es;bg);↓∃e:E. (e ↓∈ bg ∧ v ↓∈ class-le-before(X;es;e)))
Proof
Definitions occuring in Statement :
class-output: class-output(X;es;bg),
class-le-before: class-le-before(X;es;e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
class-output: class-output(X;es;bg),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
bag-member: x ↓∈ bs,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[bg:bag(E)]. \mforall{}[v:T].
uiff(v \mdownarrow{}\mmember{} class-output(X;es;bg);\mdownarrow{}\mexists{}e:E. (e \mdownarrow{}\mmember{} bg \mwedge{} v \mdownarrow{}\mmember{} class-le-before(X;es;e)))
Date html generated:
2016_05_16-PM-01_59_10
Last ObjectModification:
2016_01_17-PM-07_40_42
Theory : event-ordering
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