Nuprl Lemma : decidable__exists-classrel-between1-sv
∀[Info,T:Type].
∀X:EClass(T). ∀es:EO+(Info).
(single-valued-classrel(es;X;T) ⇒ (∀e1,e2:E. Dec(∃e:E. (e1 ≤loc e ∧ (e <loc e2) ∧ (∃v:T. v ∈ X(e))))))
Proof
Definitions occuring in Statement :
single-valued-classrel: single-valued-classrel(es;X;T),
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],
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
false: False,
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Latex:
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info).
(single-valued-classrel(es;X;T)
{}\mRightarrow{} (\mforall{}e1,e2:E. Dec(\mexists{}e:E. (e1 \mleq{}loc e \mwedge{} (e <loc e2) \mwedge{} (\mexists{}v:T. v \mmember{} X(e))))))
Date html generated:
2016_05_16-PM-01_46_26
Last ObjectModification:
2016_01_17-PM-07_46_12
Theory : event-ordering
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