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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