Nuprl Lemma : decidable__exists-classrel-between1
∀[Info,T:Type]. ∀X:EClass(T). ∀es:EO+(Info). ∀e1,e2:E. Dec(∃e:E. (e1 ≤loc e ∧ (e <loc e2) ∧ (↓∃v:T. v ∈ X(e))))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
alle-at: ∀e@i.P[e],
prop: ℙ,
existse-between1: ∃e∈[e1,e2).P[e],
exists: ∃x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
not: ¬A,
false: False,
squash: ↓T,
es-locl: (e <loc e')
Latex:
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e1,e2:E. Dec(\mexists{}e:E. (e1 \mleq{}loc e \mwedge{} (e <loc e2) \mwedge{} (\mdownarrow{}\mexists{}v:T. v \mmember{} X(e))))
Date html generated:
2016_05_16-PM-01_39_38
Last ObjectModification:
2015_12_29-PM-02_10_24
Theory : event-ordering
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