Nuprl Lemma : three-cs-vote-invariant
∀V:Type. ∀A:Id List. ∀t:ℕ+. ∀f:(V List) ⟶ V. ∀s:ts-type(three-consensus-ts(V;A;t;f)).
((ts-init(three-consensus-ts(V;A;t;f)) (ts-rel(three-consensus-ts(V;A;t;f))^*) s)
⇒ (∀a:{a:Id| (a ∈ A)} . ∀n:ℕ. ∀b:{a:Id| (a ∈ A)} . ∀v1:V.
((Vote[b;n;v1] ∈ s a) ⇒ (∃L:consensus-rcv(V;A) List. (L ≤ s b ∧ archive-condition(V;A;t;f;n;v1;L))))))
Proof
Definitions occuring in Statement :
three-consensus-ts: three-consensus-ts(V;A;t;f),
archive-condition: archive-condition(V;A;t;f;n;v;L),
cs-rcv-vote: Vote[a;i;v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
iseg: l1 ≤ l2,
l_member: (x ∈ l),
list: T List,
rel_star: R^*,
nat_plus: ℕ+,
nat: ℕ,
infix_ap: x f y,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
ts-rel: ts-rel(ts),
ts-init: ts-init(ts),
ts-type: ts-type(ts)
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
ts-reachable: ts-reachable(ts),
so_apply: x[s],
uimplies: b supposing a,
ts-type: ts-type(ts),
pi1: fst(t),
three-consensus-ts: three-consensus-ts(V;A;t;f),
and: P ∧ Q,
nat: ℕ,
exists: ∃x:A. B[x],
ts-init: ts-init(ts),
pi2: snd(t),
not: ¬A,
false: False,
ts-rel: ts-rel(ts),
infix_ap: x f y,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True,
cand: A c∧ B,
Id: Id,
sq_type: SQType(T)
Latex:
\mforall{}V:Type. \mforall{}A:Id List. \mforall{}t:\mBbbN{}\msupplus{}. \mforall{}f:(V List) {}\mrightarrow{} V. \mforall{}s:ts-type(three-consensus-ts(V;A;t;f)).
((ts-init(three-consensus-ts(V;A;t;f)) (ts-rel(three-consensus-ts(V;A;t;f))\^{}*) s)
{}\mRightarrow{} (\mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}n:\mBbbN{}. \mforall{}b:\{a:Id| (a \mmember{} A)\} . \mforall{}v1:V.
((Vote[b;n;v1] \mmember{} s a)
{}\mRightarrow{} (\mexists{}L:consensus-rcv(V;A) List. (L \mleq{} s b \mwedge{} archive-condition(V;A;t;f;n;v1;L))))))
Date html generated:
2016_05_16-PM-00_44_51
Last ObjectModification:
2016_01_17-PM-08_01_50
Theory : event-ordering
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