---

{ [V:Type]
    ((v,v':V. ((v = v')))
     (v,v':V.  Dec(v = v'))
     (A:Id List. W:{a:Id| (a  A)}  List List.
          (one-intersection(A;W)
           (s:ConsensusState. i:. v':V.
                Dec(v:V
                     (((v = v'))  in state s, inning i could commit v )))))) }

{ Proof }

---

Definitions occuring in Statement :  one-intersection: one-intersection(A;W),  cs-inning-committable: in state s, inning i could commit v ,  consensus-state4: ConsensusState,  Id: Id,  decidable: Dec(P),  uall: [x:A]. B[x],  all: x:A. B[x],  exists: x:A. B[x],  not: A,  implies: P  Q,  and: P  Q,  set: {x:A| B[x]} ,  list: type List,  int: ,  universe: Type,  equal: s = t,  l_member: (x  l)
Definitions :  uall: [x:A]. B[x],  implies: P  Q,  exists: x:A. B[x],  all: x:A. B[x],  member: t  T,  prop: ,  consensus-state4: ConsensusState,  so_lambda: x.t[x],  true: True,  iff: P  Q,  and: P  Q,  or: P  Q,  l_exists: (xL. P[x]),  rev_implies: P  Q,  cand: A c B,  guard: {T},  subtype: S  T,  not: A,  false: False,  cs-inning-committable: in state s, inning i could commit v ,  uimplies: b supposing a,  so_apply: x[s],  uiff: uiff(P;Q),  decidable: Dec(P),  cs-archived: by state s, a archived v in inning i,  fpf-domain: fpf-domain(f)
Lemmas :  consensus-state4_wf,  one-intersection_wf,  Id_wf,  l_member_wf,  decidable_wf,  not_wf,  mapfilter_wf,  list-subtype,  fpf-dom_wf,  int-deq_wf,  cs-estimate_wf,  top_wf,  subtype_rel_function,  fpf_wf,  subtype_rel_self,  subtype_rel_simple_product,  subtype-fpf2,  subtype-top,  assert_wf,  fpf-ap_wf,  decidable__l_exists_better-extract,  cs-inning-committable_wf,  decidable__cand,  decidable__not,  decidable__cs-inning-committable,  l_exists_wf,  cs-not-completed_wf,  iff_wf,  property-from-l_member,  sq_stable_from_decidable,  decidable__l_member,  decidable__equal_Id,  member-mapfilter,  member-fpf-dom,  cs-archived_wf,  decidable__cs-archived,  decidable_functionality,  decidable__or,  decidable__all-list,  decidable__implies_better,  decidable__equal_set,  decidable__cs-not-completed

---

\mforall{}[V:Type]
    ((\mexists{}v,v':V.  (\mneg{}(v  =  v')))
    {}\mRightarrow{}  (\mforall{}v,v':V.    Dec(v  =  v'))
    {}\mRightarrow{}  (\mforall{}A:Id  List.  \mforall{}W:\{a:Id|  (a  \mmember{}  A)\}    List  List.
                (one-intersection(A;W)
                {}\mRightarrow{}  (\mforall{}s:ConsensusState.  \mforall{}i:\mBbbZ{}.  \mforall{}v':V.
                            Dec(\mexists{}v:V.  ((\mneg{}(v  =  v'))  \mwedge{}  in  state  s,  inning  i  could  commit  v  ))))))


Date html generated: 2011_08_16-AM-10_02_17
Last ObjectModification: 2011_06_18-AM-09_00_31

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