Nuprl Lemma : consensus-ts4-archived-stable
∀[V:Type]
∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀a:{a:Id| (a ∈ A)} . ∀i:ℤ. ∀v:V.
ts-stable(consensus-ts4(V;A;W);s.by state s, a archived v in inning i)
Proof
Definitions occuring in Statement :
cs-archived: by state s, a archived v in inning i,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
ts-stable: ts-stable(ts;x.P[x])
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
ts-stable: ts-stable(ts;x.P[x]),
consensus-ts4: consensus-ts4(V;A;W),
ts-type: ts-type(ts),
pi1: fst(t),
ts-rel: ts-rel(ts),
pi2: snd(t),
infix_ap: x f y,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
cs-archived: by state s, a archived v in inning i,
consensus-rel: CR[x,y],
exists: ∃x:A. B[x],
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
Id: Id,
sq_type: SQType(T),
guard: {T},
cand: A c∧ B,
subtype_rel: A ⊆r B,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
fpf-domain: fpf-domain(f),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
not: ¬A,
false: False,
squash: ↓T,
true: True
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}i:\mBbbZ{}. \mforall{}v:V.
ts-stable(consensus-ts4(V;A;W);s.by state s, a archived v in inning i)
Date html generated:
2016_05_16-AM-11_59_02
Last ObjectModification:
2016_01_17-PM-03_50_58
Theory : event-ordering
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