Nuprl Lemma : consensus-state3-unequal
∀[V:Type]
((¬(INITIAL = WITHDRAWN ∈ consensus-state3(V)))
∧ (∀[v:V]
(((¬(COMMITED[v] = INITIAL ∈ consensus-state3(V))) ∧ (¬(CONSIDERING[v] = INITIAL ∈ consensus-state3(V))))
∧ (¬(COMMITED[v] = WITHDRAWN ∈ consensus-state3(V)))
∧ (¬(CONSIDERING[v] = WITHDRAWN ∈ consensus-state3(V)))
∧ (∀[v':V]
((¬(CONSIDERING[v] = COMMITED[v'] ∈ consensus-state3(V)))
∧ (¬(CONSIDERING[v] = CONSIDERING[v'] ∈ consensus-state3(V)))
∧ (¬(COMMITED[v] = COMMITED[v'] ∈ consensus-state3(V)))
supposing ¬(v = v' ∈ 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cs-withdrawn: WITHDRAWN,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),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
implies: P ⇒ Q,
cs-withdrawn: WITHDRAWN,
cs-initial: INITIAL,
consensus-state3: consensus-state3(T),
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
false: False,
prop: ℙ,
cs-commited: COMMITED[v],
isl: isl(x),
cs-considering: CONSIDERING[v],
sq_type: SQType(T),
all: ∀x:A. B[x],
true: True
Latex:
\mforall{}[V:Type]
((\mneg{}(INITIAL = WITHDRAWN))
\mwedge{} (\mforall{}[v:V]
(((\mneg{}(COMMITED[v] = INITIAL)) \mwedge{} (\mneg{}(CONSIDERING[v] = INITIAL)))
\mwedge{} (\mneg{}(COMMITED[v] = WITHDRAWN))
\mwedge{} (\mneg{}(CONSIDERING[v] = WITHDRAWN))
\mwedge{} (\mforall{}[v':V]
((\mneg{}(CONSIDERING[v] = COMMITED[v']))
\mwedge{} (\mneg{}(CONSIDERING[v] = CONSIDERING[v'])) \mwedge{} (\mneg{}(COMMITED[v] = COMMITED[v']))
supposing \mneg{}(v = v'))))))
Date html generated:
2016_05_16-AM-11_51_06
Last ObjectModification:
2015_12_29-PM-01_20_21
Theory : event-ordering
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