Nuprl Lemma : decidable__cs-inning-committable
∀[V:Type]
  ((∀v,v':V.  Dec(v = v' ∈ V))
  
⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)}  List List. ∀s:ConsensusState. ∀i:ℤ. ∀v:V.
        Dec(in state s, inning i could commit v )))
Proof
Definitions occuring in Statement : 
cs-inning-committable: in state s, inning i could commit v 
, 
consensus-state4: ConsensusState
, 
Id: Id
, 
l_member: (x ∈ l)
, 
list: T List
, 
decidable: Dec(P)
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
set: {x:A| B[x]} 
, 
int: ℤ
, 
universe: Type
, 
equal: s = t ∈ T
Lemmas : 
decidable_functionality, 
exists_wf, 
l_member_wf, 
all_wf, 
or_wf, 
cs-archived_wf, 
cs-not-completed_wf, 
l_exists_wf, 
l_exists_iff, 
decidable__l_exists_better-extract, 
decidable__all-list, 
decidable__equal_Id, 
decidable__implies, 
decidable__l_member, 
decidable__equal_set, 
set_wf, 
decidable__or, 
decidable__cs-archived, 
decidable__cs-not-completed, 
consensus-state4_wf, 
list_wf, 
Id_wf, 
decidable_wf, 
equal_wf
\mforall{}[V:Type]
    ((\mforall{}v,v':V.    Dec(v  =  v'))
    {}\mRightarrow{}  (\mforall{}A:Id  List.  \mforall{}W:\{a:Id|  (a  \mmember{}  A)\}    List  List.  \mforall{}s:ConsensusState.  \mforall{}i:\mBbbZ{}.  \mforall{}v:V.
                Dec(in  state  s,  inning  i  could  commit  v  )))
Date html generated:
2015_07_17-AM-11_28_21
Last ObjectModification:
2015_01_28-AM-01_36_16
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