{ 
[V:Type]
A:Id List. t:
. n:
. L:consensus-rcv(V;A) List. r:consensus-rcv(V;A).
(
a:{a:Id| (a 
A)}
v:V
((r = Vote[a;n;v])
(
null(filter(
r.n - 1 <z inning(r);L)))
(0 
n))) 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),
rcvd-inning-gt: i <z inning(r),
cs-rcv-vote: Vote[a;i;v],
consensus-rcv: consensus-rcv(V;A),
id-deq: IdDeq,
Id: Id,
length: ||as||,
append: as @ bs,
null: null(as),
assert: b,
nat_plus: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
le: A B,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
and: P Q,
set: {x:A| B[x]} ,
lambda: x.A[x],
cons: [car / cdr],
nil: [],
list: type List,
multiply: n * m,
subtract: n - m,
add: n + m,
natural_number: $n,
int: ,
universe: Type,
equal: s = t,
filter: filter(P;l),
l_member: (x l),
values-for-distinct: values-for-distinct(eq;L)
Definitions :
rcvd-inning-eq: inning(r) =
i,
mapfilter: mapfilter(f;P;L),
pair: <a, b>,
listp: A List,
combination: Combination(n;T),
apply-alist: apply-alist(eq;L;x),
outl: outl(x),
top: Top,
sqequal: s ~ t,
pi1: fst(t),
map: map(f;as),
remove-repeats: remove-repeats(eq;L),
cand: A c B,
fpf-cap: f(x)?z,
filter: filter(P;l),
intensional-universe: IType,
bool: 
,
iff: P 
Q,
apply: f a,
so_apply: x[s],
or: P 
Q,
guard: {T},
so_lambda: 
x.t[x],
assert: b,
tl: tl(l),
hd: hd(l),
add: n + m,
nil: [],
cons: [car / cdr],
append: as @ bs,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
union: left + right,
ge: i 
j ,
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
deq: EqDecider(T),
id-deq: IdDeq,
l_member: (x l),
votes-from-inning: votes-from-inning(i;L),
values-for-distinct: values-for-distinct(eq;L),
length: ||as||,
int_nzero: 
,
real: 
,
nat: ,
subtype: S T,
natural_number: $n,
multiply: n * m,
equal: s = t,
uall: [x:A]. B[x],
universe: Type,
Id: Id,
nat_plus: ,
int: ,
list: type List,
all: x:A. B[x],
consensus-rcv: consensus-rcv(V;A),
prop: 
,
uimplies: b supposing a,
isect: 
x:A. B[x],
exists: x:A. B[x],
product: x:A 
B[x],
set: {x:A| B[x]} ,
false: False,
void: Void,
le: A B,
not: A,
implies: P Q,
lambda: x.A[x],
less_than: a < b,
member: t T,
function: x:A 
B[x],
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
CollapseTHEN: Error :CollapseTHEN,
RepUR: Error :RepUR,
MaAuto: Error :MaAuto,
AllHyps: Error :AllHyps,
tactic: Error :tactic,
RepeatFor: Error :RepeatFor,
limited-type: LimitedType,
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
btrue: tt,
eq_atom: x =a y,
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
bimplies: p q,
band: p q,
bor: p q,
unit: Unit,
inr: inr x ,
eq_int: (i = j),
ifthenelse: if b then t else f fi ,
outr: outr(x),
spreadn: spread3,
grp_car: |g|,
bnot: b,
list_ind: list_ind def,
atom: Atom,
sq_type: SQType(T),
rev_implies: P Q,
last: last(L),
select: l[i],
atom: Atom$n,
l_all: (xL.P[x]),
subtract: n - m,
rcvd-inning-gt: i <z inning(r),
null: null(as),
cs-rcv-vote: Vote[a;i;v],
inl: inl x ,
rcv-vote?: rcv-vote?(x),
rcvd-vote: rcvd-vote(x),
rationals: 
,
minus: -n,
it: 
,
remove_repeats_nil: remove_repeats_nil{remove_repeats_nil_compseq_tag_def:o}(eq),
remove_repeats_cons: remove_repeats_cons{remove_repeats_cons_compseq_tag_def:o}(v; u; eq)
Lemmas :
list_subtype_base,
set_subtype_base,
assert_of_null,
votes-from-inning-is-nil,
cs-rcv-vote_wf,
append-nil,
list-set-type2,
l_all_wf,
nat_wf,
l_member-settype,
l_member_subtype,
subtype_base_sq,
atom2_subtype_base,
iff_weakening_uiff,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
eq_int_wf,
nat_properties,
filter_wf,
pos_length2,
null_wf3,
filter_wf_top,
rcvd-inning-gt_wf,
bnot_wf,
Id_wf,
l_member_wf,
deq_wf,
member_wf,
id-deq_wf,
subtype_rel_wf,
votes-from-inning_wf,
values-for-distinct_wf,
length_wf1,
le_wf,
consensus-rcv_wf,
nat_plus_wf,
append_wf,
length_wf_nat,
assert_wf,
not_wf,
uall_wf,
uiff_inversion,
nat_plus_properties,
iff_wf,
bool_wf,
intensional-universe_wf,
list-subtype,
strong-subtype-deq-subtype,
strong-subtype_wf,
strong-subtype-set3,
strong-subtype-self,
false_wf,
remove-repeats_wf,
length-map,
map_wf,
pi1_wf_top,
top_wf,
mapfilter-append,
rcvd-inning-eq_wf,
map_append_sq
\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).
(\mexists{}a:\{a:Id| (a \mmember{} A)\}
\mexists{}v:V. ((r = Vote[a;n;v]) \mwedge{} (\mneg{}\muparrow{}null(filter(\mlambda{}r.n - 1 <z inning(r);L))) \mwedge{} (0 \mleq{} n))) 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:
2011_08_16-AM-10_12_45
Last ObjectModification:
2011_06_18-AM-09_04_55
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