Nuprl Lemma : es-hist-partition
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e1,e2,e:E].
(es-hist(es;e1;e2) = (es-hist(es;e1;pred(e)) @ es-hist(es;e;e2)) ∈ (Info List)) supposing (e ≤loc e2 and (e1 <loc e))
Proof
Definitions occuring in Statement :
es-hist: es-hist(es;e1;e2),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-pred: pred(e),
es-E: E,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-hist: es-hist(es;e1;e2),
top: Top,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
and: P ∧ Q,
cand: A c∧ B
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e1,e2,e:E].
(es-hist(es;e1;e2) = (es-hist(es;e1;pred(e)) @ es-hist(es;e;e2))) supposing
(e \mleq{}loc e2 and
(e1 <loc e))
Date html generated:
2016_05_16-PM-01_19_27
Last ObjectModification:
2016_01_17-PM-07_55_15
Theory : event-ordering
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