Nuprl Lemma : consensus-state4-exclusive-cases
∀[V:Type]
∀A:Id List. ∀s:ConsensusState. ∀a:{a:Id| (a ∈ A)} . ∀i:ℤ.
((by state s, a passed inning i without archiving a value
∧ (¬in state s, a has not completed inning i)
∧ (∀v:V. (¬by state s, a archived v in inning i)))
∨ (in state s, a has not completed inning i
∧ (¬by state s, a passed inning i without archiving a value)
∧ (∀v:V. (¬by state s, a archived v in inning i)))
∨ (∃v:V
(by state s, a archived v in inning i
∧ (¬by state s, a passed inning i without archiving a value)
∧ (¬in state s, a has not completed inning i)
∧ (∀v':V. ¬by state s, a archived v' in inning i supposing ¬(v' = v ∈ V)))))
Proof
Definitions occuring in Statement :
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
consensus-state4: ConsensusState,
Id: Id,
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
or: 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],
member: t ∈ T,
all: ∀x:A. B[x],
or: P ∨ Q,
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
guard: {T},
cs-not-completed: in state s, a has not completed inning i,
le: A ≤ B,
exists: ∃x:A. B[x],
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b,
squash: ↓T
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}s:ConsensusState. \mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}i:\mBbbZ{}.
((by state s, a passed inning i without archiving a value
\mwedge{} (\mneg{}in state s, a has not completed inning i)
\mwedge{} (\mforall{}v:V. (\mneg{}by state s, a archived v in inning i)))
\mvee{} (in state s, a has not completed inning i
\mwedge{} (\mneg{}by state s, a passed inning i without archiving a value)
\mwedge{} (\mforall{}v:V. (\mneg{}by state s, a archived v in inning i)))
\mvee{} (\mexists{}v:V
(by state s, a archived v in inning i
\mwedge{} (\mneg{}by state s, a passed inning i without archiving a value)
\mwedge{} (\mneg{}in state s, a has not completed inning i)
\mwedge{} (\mforall{}v':V. \mneg{}by state s, a archived v' in inning i supposing \mneg{}(v' = v)))))
Date html generated:
2016_05_16-AM-11_58_48
Last ObjectModification:
2016_01_17-PM-03_51_52
Theory : event-ordering
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