Nuprl Lemma : decidable__cs-committed-change
∀[V:Type]
((∃v,v':V. (¬(v = v' ∈ V)))
⇒ (∀v,v':V. Dec(v = v' ∈ V))
⇒ (∀L:V List. Dec(∃v:V. (¬(v ∈ L))))
⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List.
(one-intersection(A;W)
⇒ (∀i:ℤ. ∀x,y:ConsensusState.
Dec(∃v:V. (in state x, inning i could commit v ∧ (¬in state y, inning i could commit v )))))))
Proof
Definitions occuring in Statement :
one-intersection: one-intersection(A;W),
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],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
guard: {T}
Latex:
\mforall{}[V:Type]
((\mexists{}v,v':V. (\mneg{}(v = v')))
{}\mRightarrow{} (\mforall{}v,v':V. Dec(v = v'))
{}\mRightarrow{} (\mforall{}L:V List. Dec(\mexists{}v:V. (\mneg{}(v \mmember{} L))))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List.
(one-intersection(A;W)
{}\mRightarrow{} (\mforall{}i:\mBbbZ{}. \mforall{}x,y:ConsensusState.
Dec(\mexists{}v:V
(in state x, inning i could commit v
\mwedge{} (\mneg{}in state y, inning i could commit v )))))))
Date html generated:
2016_05_16-PM-00_12_22
Last ObjectModification:
2015_12_29-PM-01_29_19
Theory : event-ordering
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