Nuprl Lemma : decidable__cs-archived
∀[V:Type]
∀A:Id List. ∀s:ConsensusState. ∀a:{a:Id| (a ∈ A)} . ∀i:ℤ. ∀v:V.
((∀v,v':V. Dec(v = v' ∈ V)) ⇒ Dec(by state s, a archived v in inning i))
Proof
Definitions occuring in Statement :
cs-archived: by state s, a archived v in inning i,
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
cs-archived: by state s, a archived v in inning i,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
fpf-domain: fpf-domain(f)
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}s:ConsensusState. \mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}i:\mBbbZ{}. \mforall{}v:V.
((\mforall{}v,v':V. Dec(v = v')) {}\mRightarrow{} Dec(by state s, a archived v in inning i))
Date html generated:
2016_05_16-AM-11_58_00
Last ObjectModification:
2015_12_29-PM-01_20_06
Theory : event-ordering
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