{ 
[V:Type]. [A:Id List]. [t:
]. [n1:]. [n2:
]. [v1:V].
[L1:consensus-rcv(V;A) List]. [a:{a:Id| (a 
A)} ].
({(n1 = n2) 
(
null(filter(
r.n1 - 1 <z inning(r);L1)))}) supposing
((((2 * t) + 1) 
||values-for-distinct(IdDeq;votes-from-inning(n2;L1
@ [Vote[a;n1;v1]]))||) and
(||values-for-distinct(IdDeq;votes-from-inning(n2;L1))|| (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: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T},
le: A B,
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 :
top: Top,
subtract: n - m,
rcvd-inning-gt: i <z inning(r),
null: null(as),
axiom: Ax,
pair: <a, b>,
guard: {T},
tl: tl(l),
hd: hd(l),
void: Void,
cs-rcv-vote: Vote[a;i;v],
nil: [],
cons: [car / cdr],
append: as @ bs,
add: n + m,
lambda: x.A[x],
so_lambda: 
x.t[x],
cand: A c B,
fpf-cap: f(x)?z,
filter: filter(P;l),
intensional-universe: IType,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
and: P Q,
uiff: uiff(P;Q),
int_nzero: 
,
real: 
,
subtype: S 
T,
natural_number: $n,
multiply: n * m,
subtype_rel: A r B,
fpf: a:A fp-> B[a],
product: x:A 
B[x],
exists: 
x:A. B[x],
less_than: a < b,
implies: P 
Q,
false: False,
not: A,
bool: 
,
assert: b,
iff: P 
Q,
deq: EqDecider(T),
id-deq: IdDeq,
votes-from-inning: votes-from-inning(i;L),
values-for-distinct: values-for-distinct(eq;L),
length: ||as||,
le: A B,
uimplies: b supposing a,
prop: 
,
l_member: (x l),
isect: 
x:A. B[x],
consensus-rcv: consensus-rcv(V;A),
int: ,
set: {x:A| B[x]} ,
nat: ,
all: x:A. B[x],
function: x:A 
B[x],
uall: [x:A]. B[x],
nat_plus: ,
universe: Type,
member: t T,
Id: Id,
list: type List,
equal: s = t,
tactic: Error :tactic,
apply: f a,
so_apply: x[s],
union: left + right,
or: P 
Q,
fpf-dom: x dom(f),
grp_car: |g|,
squash: 
T,
IdLnk: IdLnk,
locl: locl(a),
Knd: Knd,
pi2: snd(t),
pi1: fst(t),
rev_implies: P Q,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$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,
isl: isl(x),
bimplies: p q,
band: p q,
bor: p q,
inl: inl x ,
sq_type: SQType(T),
rationals: 
,
true: True,
bnot: b,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
limited-type: LimitedType,
outr: outr(x),
inr: inr x
Lemmas :
subtype_base_sq,
int_subtype_base,
outr_wf,
true_wf,
bnot_wf,
ifthenelse_wf,
top_wf,
iff_weakening_uiff,
assert_of_bnot,
isl_wf,
pi1_wf_top,
pi2_wf,
pos_length2,
filter_wf,
uiff_inversion,
consensus-rcv-crosses-threshold,
bool_wf,
id-deq_wf,
member_wf,
Id_wf,
l_member_wf,
deq_wf,
iff_wf,
assert_wf,
values-for-distinct_wf,
votes-from-inning_wf,
length_wf1,
le_wf,
consensus-rcv_wf,
nat_wf,
nat_plus_wf,
subtype_rel_wf,
false_wf,
intensional-universe_wf,
length_wf_nat,
list-subtype,
strong-subtype-deq-subtype,
strong-subtype_wf,
strong-subtype-set3,
strong-subtype-self,
nat_plus_properties,
cs-rcv-vote_wf,
append_wf,
guard_wf,
not_wf,
null_wf3,
filter_wf_top,
rcvd-inning-gt_wf
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[n1:\mBbbN{}]. \mforall{}[n2:\mBbbZ{}]. \mforall{}[v1:V]. \mforall{}[L1:consensus-rcv(V;A) List].
\mforall{}[a:\{a:Id| (a \mmember{} A)\} ].
(\{(n1 = n2) \mwedge{} (\mneg{}\muparrow{}null(filter(\mlambda{}r.n1 - 1 <z inning(r);L1)))\}) supposing
((((2 * t) + 1) \mleq{} ||values-for-distinct(IdDeq;votes-from-inning(n2;L1
@ [Vote[a;n1;v1]]))||) and
(||values-for-distinct(IdDeq;votes-from-inning(n2;L1))|| \mleq{} (2 * t)))
Date html generated:
2011_08_16-AM-10_13_25
Last ObjectModification:
2011_06_18-AM-09_06_05
Home
Index