Nuprl Lemma : votes-from-inning-is-nil
∀[V:Type]. ∀[A:Id List]. ∀[L:consensus-rcv(V;A) List]. ∀[i,n:ℤ].
(votes-from-inning(i;L) ~ []) supposing (n < i and (filter(λr.n <z inning(r);L) = [] ∈ (consensus-rcv(V;A) List)))
Proof
Definitions occuring in Statement :
votes-from-inning: votes-from-inning(i;L),
rcvd-inning-gt: i <z inning(r),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
filter: filter(P;l),
nil: [],
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
int: ℤ,
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
votes-from-inning: votes-from-inning(i;L),
mapfilter: mapfilter(f;P;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
less_than: a < b,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
consensus-rcv: consensus-rcv(V;A),
rcvd-inning-gt: i <z inning(r),
rcvd-inning-eq: inning(r) =z i,
rcvd-vote: rcvd-vote(x),
rcv-vote?: rcv-vote?(x),
outr: outr(x),
bfalse: ff,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
assert: ↑b,
spreadn: spread3,
btrue: tt,
nat: ℕ,
ge: i ≥ j ,
uiff: uiff(P;Q)
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[L:consensus-rcv(V;A) List]. \mforall{}[i,n:\mBbbZ{}].
(votes-from-inning(i;L) \msim{} []) supposing (n < i and (filter(\mlambda{}r.n <z inning(r);L) = []))
Date html generated:
2016_05_16-PM-00_35_37
Last ObjectModification:
2016_01_17-PM-03_56_51
Theory : event-ordering
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