Nuprl Lemma : consensus-rcv-crosses-size
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[n:ℤ]. ∀[L:consensus-rcv(V;A) List]. ∀[r:consensus-rcv(V;A)].
(||remove-repeats(IdDeq;map(λp.(fst(p));votes-from-inning(n;L @ [r])))|| = ((2 * t) + 1) ∈ ℤ) supposing
((((2 * t) + 1) ≤ ||values-for-distinct(IdDeq;votes-from-inning(n;L @ [r]))||) and
(||values-for-distinct(IdDeq;votes-from-inning(n;L))|| ≤ (2 * t)))
Proof
Definitions occuring in Statement :
votes-from-inning: votes-from-inning(i;L),
consensus-rcv: consensus-rcv(V;A),
id-deq: IdDeq,
Id: Id,
values-for-distinct: values-for-distinct(eq;L),
remove-repeats: remove-repeats(eq;L),
length: ||as||,
map: map(f;as),
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
le: A ≤ B,
lambda: λx.A[x],
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
values-for-distinct: values-for-distinct(eq;L),
top: Top,
prop: ℙ,
pi1: fst(t),
subtype_rel: A ⊆r B,
votes-from-inning: votes-from-inning(i;L),
le: A ≤ B,
and: P ∧ Q,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
rcvd-inning-eq: inning(r) =z i,
rcvd-vote: rcvd-vote(x),
mapfilter: mapfilter(f;P;L),
rcv-vote?: rcv-vote?(x),
consensus-rcv: consensus-rcv(V;A),
outr: outr(x),
bfalse: ff,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
spreadn: spread3,
btrue: tt,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
nat: ℕ,
ge: i ≥ j ,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
decidable: Dec(P)
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[n:\mBbbZ{}]. \mforall{}[L:consensus-rcv(V;A) List]. \mforall{}[r:consensus-rcv(V;A)].
(||remove-repeats(IdDeq;map(\mlambda{}p.(fst(p));votes-from-inning(n;L @ [r])))||
= ((2 * t) + 1)) supposing
((((2 * t) + 1) \mleq{} ||values-for-distinct(IdDeq;votes-from-inning(n;L @ [r]))||) and
(||values-for-distinct(IdDeq;votes-from-inning(n;L))|| \mleq{} (2 * t)))
Date html generated:
2016_05_16-PM-00_39_12
Last ObjectModification:
2016_01_17-PM-08_00_54
Theory : event-ordering
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