Nuprl Lemma : consensus-event-cases
∀[V:Type]
∀A:Id List. ∀e:consensus-event(V;A).
((e = NextInning ∈ consensus-event(V;A))
∨ (∃v:V. (e = Archive(v) ∈ consensus-event(V;A)))
∨ (∃b:{a:Id| (a ∈ A)} . ∃i:ℕ. ∃z:ℕi × V?. (e = consensus-message(b;i;z) ∈ consensus-event(V;A))))
Proof
Definitions occuring in Statement :
consensus-message: consensus-message(b;i;z),
archive-event: Archive(v),
inning-event: NextInning,
consensus-event: consensus-event(V;A),
Id: Id,
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
unit: Unit,
set: {x:A| B[x]} ,
product: x:A × B[x],
union: left + right,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
consensus-event: consensus-event(V;A),
or: P ∨ Q,
inning-event: NextInning,
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
archive-event: Archive(v),
exists: ∃x:A. B[x],
consensus-message: consensus-message(b;i;z)
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}e:consensus-event(V;A).
((e = NextInning)
\mvee{} (\mexists{}v:V. (e = Archive(v)))
\mvee{} (\mexists{}b:\{a:Id| (a \mmember{} A)\} . \mexists{}i:\mBbbN{}. \mexists{}z:\mBbbN{}i \mtimes{} V?. (e = consensus-message(b;i;z))))
Date html generated:
2016_05_16-PM-00_28_29
Last ObjectModification:
2016_01_17-PM-03_55_54
Theory : event-ordering
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