Nuprl Lemma : decidable__cs-precondition
∀[V:Type]
((∀v1,v2:V. Dec(v1 = v2 ∈ V))
⇒ (∃v,v':V. (¬(v = v' ∈ V)))
⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀s:ConsensusState. ∀i:ℤ. ∀v:V.
Dec(state s may consider v in inning i)))
Proof
Definitions occuring in Statement :
cs-precondition: state s may consider 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],
exists: ∃x:A. B[x],
not: ¬A,
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],
implies: P ⇒ Q,
all: ∀x:A. B[x],
cs-precondition: state s may consider v in inning i,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
consensus-state4: ConsensusState,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
Id: Id,
sq_type: SQType(T),
guard: {T},
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
sq_stable: SqStable(P),
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B
Latex:
\mforall{}[V:Type]
((\mforall{}v1,v2:V. Dec(v1 = v2))
{}\mRightarrow{} (\mexists{}v,v':V. (\mneg{}(v = v')))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}s:ConsensusState. \mforall{}i:\mBbbZ{}. \mforall{}v:V.
Dec(state s may consider v in inning i)))
Date html generated:
2016_05_16-PM-00_04_07
Last ObjectModification:
2016_01_17-PM-03_55_13
Theory : event-ordering
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