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
Lemmas :
cs-inning-committable-some2,
consensus-state4_wf,
one-intersection_wf,
list_wf,
Id_wf,
l_member_wf,
all_wf,
decidable_wf,
exists_wf,
not_wf,
equal_wf,
cs-inning-committable_wf,
l_exists_iff,
cs-not-completed_wf,
set_wf,
decidable__l_exists_better-extract,
decidable__cand,
decidable__cs-inning-committable,
decidable__not,
decidable__all-list,
decidable__equal_Id,
decidable__implies_better,
decidable__l_member,
decidable__equal_set,
decidable__cs-not-completed,
decidable_functionality,
or_wf,
l_exists_wf,
iff_wf
\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:
2015_07_17-AM-11_35_39
Last ObjectModification:
2015_07_16-AM-10_14_52
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