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  ((¬(INITIAL = WITHDRAWN ∈ consensus-state3(V)))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       ∧ (¬(COMMITED[v] = WITHDRAWN ∈ consensus-state3(V)))
       ∧ (¬(CONSIDERING[v] = WITHDRAWN ∈ consensus-state3(V)))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cs-withdrawn: WITHDRAWN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cs-withdrawn: WITHDRAWN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    ((\mneg{}(INITIAL  =  WITHDRAWN))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              \mwedge{}  (\mneg{}(COMMITED[v]  =  WITHDRAWN))
              \mwedge{}  (\mneg{}(CONSIDERING[v]  =  WITHDRAWN))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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