Nuprl Lemma : three-cs-no-repeated-votes
∀V:Type. ∀A:Id List. ∀t:ℕ+. ∀f:(V List) ⟶ V. ∀s:ts-reachable(three-consensus-ts(V;A;t;f)). ∀a:{a:Id| (a ∈ A)} .
no_repeats(consensus-rcv(V;A);filter(λx.rcv-vote?(x);s a))
Proof
Definitions occuring in Statement :
three-consensus-ts: three-consensus-ts(V;A;t;f),
rcv-vote?: rcv-vote?(x),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
filter: filter(P;l),
list: T List,
nat_plus: ℕ+,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
ts-reachable: ts-reachable(ts)
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
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),
implies: P ⇒ Q,
guard: {T},
ts-init: ts-init(ts),
pi2: snd(t),
top: Top,
infix_ap: x f y,
ts-rel: ts-rel(ts),
exists: ∃x:A. B[x],
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
Id: Id,
sq_type: SQType(T),
uiff: uiff(P;Q),
cand: A c∧ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
consensus-rcv: consensus-rcv(V;A),
rcv-vote?: rcv-vote?(x),
cs-rcv-vote: Vote[a;i;v],
squash: ↓T,
true: True,
rev_implies: P ⇐ Q
Latex:
\mforall{}V:Type. \mforall{}A:Id List. \mforall{}t:\mBbbN{}\msupplus{}. \mforall{}f:(V List) {}\mrightarrow{} V. \mforall{}s:ts-reachable(three-consensus-ts(V;A;t;f)).
\mforall{}a:\{a:Id| (a \mmember{} A)\} .
no\_repeats(consensus-rcv(V;A);filter(\mlambda{}x.rcv-vote?(x);s a))
Date html generated:
2016_05_16-PM-00_46_50
Last ObjectModification:
2016_01_17-PM-07_59_13
Theory : event-ordering
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