Nuprl Lemma : rcvd-innings-nil
∀[V:Type]. ∀[A:Id List]. ∀[L:consensus-rcv(V;A) List]. ∀[i,n:ℤ].
(filter(λr.i <z inning(r);L) ~ []) supposing
((n ≤ i) and
(filter(λr.n <z inning(r);L) = [] ∈ (consensus-rcv(V;A) List)))
Proof
Definitions occuring in Statement :
rcvd-inning-gt: i <z inning(r),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
filter: filter(P;l),
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
lambda: λx.A[x],
int: ℤ,
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
cand: A c∧ B,
consensus-rcv: consensus-rcv(V;A),
rcvd-inning-gt: i <z inning(r),
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 ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
uiff: uiff(P;Q)
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[L:consensus-rcv(V;A) List]. \mforall{}[i,n:\mBbbZ{}].
(filter(\mlambda{}r.i <z inning(r);L) \msim{} []) supposing ((n \mleq{} i) and (filter(\mlambda{}r.n <z inning(r);L) = []))
Date html generated:
2016_05_16-PM-00_35_50
Last ObjectModification:
2016_01_17-PM-03_57_01
Theory : event-ordering
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