Nuprl Lemma : new_23_sig_quorum_inv_vote_fun
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e:E. ∀ni:ℤ × ℤ. ∀i:ℕ||snd(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))||.
  (↓∃e':E
     ((e' <loc e)
     ∧ <<ni, fst(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]>
       , snd(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]
       > ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(e')))
Proof
Definitions occuring in Statement : 
new_23_sig_QuorumStateFun: new_23_sig_QuorumStateFun(Cmd;notify;propose;f;x;es;e)
, 
new_23_sig_vote'base: new_23_sig_vote'base(Cmd;notify;propose;f)
, 
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose)
, 
Message: Message(f)
, 
classrel: v ∈ X(e)
, 
event-ordering+: EO+(Info)
, 
es-locl: (e <loc e')
, 
es-E: E
, 
Id: Id
, 
select: L[n]
, 
length: ||as||
, 
list: T List
, 
int_seg: {i..j-}
, 
vatype: ValueAllType
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
squash: ↓T
, 
and: P ∧ Q
, 
pair: <a, b>
, 
product: x:A × B[x]
, 
natural_number: $n
, 
int: ℤ
, 
atom: Atom
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
subtype_rel: A ⊆r B
, 
vatype: ValueAllType
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
top: Top
, 
squash: ↓T
, 
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose)
, 
prop: ℙ
Latex:
\mforall{}Cmd:ValueAllType.  \mforall{}notify,propose:Atom  List.  \mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).
\mforall{}es:EO+(Message(f)).  \mforall{}e:E.  \mforall{}ni:\mBbbZ{}  \mtimes{}  \mBbbZ{}.
\mforall{}i:\mBbbN{}||snd(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))||.
    (\mdownarrow{}\mexists{}e':E
          ((e'  <loc  e)
          \mwedge{}  <<ni,  fst(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]>
              ,  snd(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]
              >  \mmember{}  new\_23\_sig\_vote'base(Cmd;notify;propose;f)(e')))
Date html generated:
2016_05_17-PM-02_15_08
Last ObjectModification:
2016_01_18-AM-09_32_05
Theory : 2!3!consensus!with!signatures
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