Nuprl Lemma : no-classrel-iff-empty
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. uiff(∀v:T. (¬v ∈ X(e));(X es e) = {} ∈ bag(T))
Proof
Definitions occuring in Statement :
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],
all: ∀x:A. B[x],
not: ¬A,
apply: f a,
universe: Type,
equal: s = t ∈ T,
empty-bag: {},
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
classrel: v ∈ X(e)
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. uiff(\mforall{}v:T. (\mneg{}v \mmember{} X(e));(X es e) = \{\})
Date html generated:
2016_05_16-PM-02_02_17
Last ObjectModification:
2015_12_29-PM-02_23_36
Theory : event-ordering
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