Nuprl Lemma : consensus-state4-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))
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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
cs-passed: by state s, a passed inning i without archiving a value,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
fpf-domain: fpf-domain(f),
cand: A c∧ B,
guard: {T},
false: False,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla)
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
\mvee{} in state s, a has not completed inning i
\mvee{} (\mexists{}v:V. by state s, a archived v in inning i))
Date html generated:
2016_05_16-AM-11_58_37
Last ObjectModification:
2016_01_17-PM-03_50_49
Theory : event-ordering
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