Nuprl Lemma : rsc4_voter_start_unique

Cmd:ValueAllType. eq:EqDecider(Cmd). locs,clients:bag(Id). es:EO'. n,max1,max2:. missing1,missing2: List.
e1,e2:E. c1,c2:Cmd.
  (<max1, missing1 rsc4_ReplicaState(Cmd)(e1)
   ((max1 < n)  (n  missing1))
   <n, c1 rsc4_Proposal(Cmd)(e1)
   <max2, missing2 rsc4_ReplicaState(Cmd)(e2)
   ((max2 < n)  (n  missing2))
   <n, c2 rsc4_Proposal(Cmd)(e2)
   (loc(e1) = loc(e2))
   (e1 = e2))


Proof




Definitions occuring in Statement :  rsc4_ReplicaState: rsc4_ReplicaState(Cmd) rsc4_Proposal: rsc4_Proposal(Cmd) Message: Message classrel: v  X(e) event-ordering+: EO+(Info) es-loc: loc(e) es-E: E Id: Id all: x:A. B[x] implies: P  Q or: P  Q less_than: a < b pair: <a, b> product: x:A  B[x] list: type List int: equal: s = t l_member: (x  l) deq: EqDecider(T) bag: bag(T) vatype: ValueAllType
Definitions :  guard: {T} so_lambda: x.t[x] prop: false: False and: P  Q member: t  T iff: P  Q rev_implies: P  Q implies: P  Q vatype: ValueAllType all: x:A. B[x] uimplies: b supposing a so_apply: x[s] not: A le: A  B uall: [x:A]. B[x] or: P  Q subtype: S  T
Lemmas :  valueall-type_wf deq_wf bag_wf event-ordering+_wf es-E_wf rsc4_ReplicaState_wf rsc4_Proposal_wf classrel_wf Message_wf es-loc_wf Id_wf equal_wf assert_of_lt_int or_functionality_wrt_iff implies_functionality_wrt_iff all_functionality_wrt_iff assert_of_le_int iff_weakening_uiff assert-int-list-member not_functionality_wrt_iff less_than_wf l_member_wf lt_int_wf or_wf all_wf le_int_wf int-list-member_wf assert_wf not_wf and_wf le_wf and_functionality_wrt_iff rsc4_replica_state_mem event-ordering+_inc es-locl-trichotomy

\mforall{}Cmd:ValueAllType.  \mforall{}eq:EqDecider(Cmd).  \mforall{}locs,clients:bag(Id).  \mforall{}es:EO'.  \mforall{}n,max1,max2:\mBbbZ{}.
\mforall{}missing1,missing2:\mBbbZ{}  List.  \mforall{}e1,e2:E.  \mforall{}c1,c2:Cmd.
    (<max1,  missing1>  \mmember{}  rsc4\_ReplicaState(Cmd)(e1)
    {}\mRightarrow{}  ((max1  <  n)  \mvee{}  (n  \mmember{}  missing1))
    {}\mRightarrow{}  <n,  c1>  \mmember{}  rsc4\_Proposal(Cmd)(e1)
    {}\mRightarrow{}  <max2,  missing2>  \mmember{}  rsc4\_ReplicaState(Cmd)(e2)
    {}\mRightarrow{}  ((max2  <  n)  \mvee{}  (n  \mmember{}  missing2))
    {}\mRightarrow{}  <n,  c2>  \mmember{}  rsc4\_Proposal(Cmd)(e2)
    {}\mRightarrow{}  (loc(e1)  =  loc(e2))
    {}\mRightarrow{}  (e1  =  e2))


Date html generated: 2012_02_20-PM-04_58_57
Last ObjectModification: 2012_02_02-PM-03_39_09

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