Nuprl Lemma : consensus-state3-cases
∀[V:Type]
∀x:consensus-state3(V)
(((x = INITIAL ∈ consensus-state3(V)) ∨ (x = WITHDRAWN ∈ consensus-state3(V)))
∨ (∃v:V. ((x = CONSIDERING[v] ∈ consensus-state3(V)) ∨ (x = COMMITED[v] ∈ consensus-state3(V)))))
Proof
Definitions occuring in Statement :
cs-commited: COMMITED[v],
cs-considering: CONSIDERING[v],
cs-withdrawn: WITHDRAWN,
cs-initial: INITIAL,
consensus-state3: consensus-state3(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
consensus-state3: consensus-state3(T),
cs-commited: COMMITED[v],
guard: {T},
or: P ∨ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
cs-considering: CONSIDERING[v],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
cs-withdrawn: WITHDRAWN,
so_lambda: λ2x.t[x],
so_apply: x[s],
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
false: False,
cs-initial: INITIAL
Latex:
\mforall{}[V:Type]
\mforall{}x:consensus-state3(V)
(((x = INITIAL) \mvee{} (x = WITHDRAWN)) \mvee{} (\mexists{}v:V. ((x = CONSIDERING[v]) \mvee{} (x = COMMITED[v]))))
Date html generated:
2016_05_16-AM-11_51_15
Last ObjectModification:
2016_01_17-PM-03_50_01
Theory : event-ordering
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