Nuprl Lemma : class-output-member-support
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[bg:bag(E)]. ∀[x:T]. ∀[X:EClass(T)].
↓∃e:E. (e ↓∈ class-output-support(es;bg) ∧ x ∈ X(e)) supposing x ↓∈ class-output(X;es;bg)
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
class-output-support: class-output-support(es;bg),
class-output: class-output(X;es;bg),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
squash: ↓T,
exists: ∃x:A. B[x],
cand: A c∧ B,
class-output-support: class-output-support(es;bg),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
rev_uimplies: rev_uimplies(P;Q),
bag-member: x ↓∈ bs,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Latex:
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[bg:bag(E)]. \mforall{}[x:T]. \mforall{}[X:EClass(T)].
\mdownarrow{}\mexists{}e:E. (e \mdownarrow{}\mmember{} class-output-support(es;bg) \mwedge{} x \mmember{} X(e)) supposing x \mdownarrow{}\mmember{} class-output(X;es;bg)
Date html generated:
2016_05_16-PM-01_59_37
Last ObjectModification:
2016_01_17-PM-07_40_29
Theory : event-ordering
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