Nuprl Lemma : new_23_sig_assert_newvote
∀[Cmd:ValueAllType]
  ∀ni:ℤ × ℤ. ∀vote:ℤ × ℤ × Cmd × Id. ∀quorum:Cmd List × (Id List).
    (↑(new_23_sig_newvote(Cmd) ni vote quorum) 
⇐⇒ (ni = (fst(fst(vote))) ∈ (ℤ × ℤ)) ∧ (¬(snd(vote) ∈ snd(quorum))))
Proof
Definitions occuring in Statement : 
new_23_sig_newvote: new_23_sig_newvote(Cmd)
, 
Id: Id
, 
l_member: (x ∈ l)
, 
list: T List
, 
vatype: ValueAllType
, 
assert: ↑b
, 
uall: ∀[x:A]. B[x]
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
not: ¬A
, 
and: P ∧ Q
, 
apply: f a
, 
product: x:A × B[x]
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
vatype: ValueAllType
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
new_23_sig_newvote: new_23_sig_newvote(Cmd)
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
top: Top
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
false: False
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
uiff: uiff(P;Q)
Latex:
\mforall{}[Cmd:ValueAllType]
    \mforall{}ni:\mBbbZ{}  \mtimes{}  \mBbbZ{}.  \mforall{}vote:\mBbbZ{}  \mtimes{}  \mBbbZ{}  \mtimes{}  Cmd  \mtimes{}  Id.  \mforall{}quorum:Cmd  List  \mtimes{}  (Id  List).
        (\muparrow{}(new\_23\_sig\_newvote(Cmd)  ni  vote  quorum)
        \mLeftarrow{}{}\mRightarrow{}  (ni  =  (fst(fst(vote))))  \mwedge{}  (\mneg{}(snd(vote)  \mmember{}  snd(quorum))))
Date html generated:
2016_05_17-PM-02_25_53
Last ObjectModification:
2015_12_29-PM-08_06_07
Theory : 2!3!consensus!with!signatures
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