{ 
[V:Type]. [A:Id List]. [W:{a:Id| (a 
A)} List List]. [a:{a:Id| (a A)} \000C].
[x:ts-reachable(consensus-ts4(V;A;W))]. [i:
].
i 
Inning(x;a) supposing (i fpf-domain(Estimate(x;a))) }
{ Proof }
Definitions occuring in Statement :
consensus-ts4: consensus-ts4(V;A;W),
cs-estimate: Estimate(s;a),
cs-inning: Inning(s;a),
fpf-domain: fpf-domain(f),
Id: Id,
uimplies: b supposing a,
uall: [x:A]. B[x],
le: A B,
set: {x:A| B[x]} ,
list: type List,
int: ,
universe: Type,
l_member: (x l),
ts-reachable: ts-reachable(ts)
Definitions :
spread: spread def,
pi1: fst(t),
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
l_contains: A 
B,
reducible: reducible(a),
prime: prime(a),
l_exists: (
xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
decidable: Dec(P),
iff: P 
Q,
squash: 
T,
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
assert: 
b,
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
sq_stable: SqStable(P),
guard: {T},
true: True,
fpf-cap: f(x)?z,
so_lambda: 
x.t[x],
filter: filter(P;l),
intensional-universe: IType,
select: l[i],
length: ||as||,
real: 
,
grp_car: |g|,
subtype: S T,
nat: 
,
cand: A c
B,
fpf-single: x : v,
bool: 
,
fpf-empty: 
,
natural_number: $n,
minus: -n,
pair: <a, b>,
ts-init: ts-init(ts),
consensus-rel: CR[x,y],
rel_star: R^*,
cs-inning: Inning(s;a),
ts-rel: ts-rel(ts),
lambda: x.A[x],
void: Void,
false: False,
implies: P Q,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
apply: f a,
infix_ap: x f y,
exists: x:A. B[x],
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
consensus-state4: ConsensusState,
top: Top,
cs-estimate: Estimate(s;a),
fpf-domain: fpf-domain(f),
uimplies: b supposing a,
int: ,
ts-type: ts-type(ts),
subtype_rel: A r B,
consensus-ts4: consensus-ts4(V;A;W),
ts-reachable: ts-reachable(ts),
prop: 
,
Id: Id,
universe: Type,
list: type List,
set: {x:A| B[x]} ,
l_member: (x l),
equal: s = t,
all: x:A. B[x],
function: x:A 
B[x],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
Auto: Error :Auto,
Complete: Error :Complete,
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
RepeatFor: Error :RepeatFor,
MaAuto: Error :MaAuto,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic,
transition-system: transition-system{i:l},
so_apply: x[s],
union: left + right,
or: P 
Q,
bag: bag(T),
deq: EqDecider(T),
ma-state: State(ds),
fpf-dom: x dom(f),
tag-by: zT,
rev_implies: P Q,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
b-union: A 
B,
nil: [],
RepUR: Error :RepUR,
int-deq: IntDeq,
fpf-join: f 
g,
cs-precondition: state s may consider v in inning i,
add: n + m,
limited-type: LimitedType,
imax: imax(a;b),
cons: [car / cdr],
IdLnk: IdLnk,
consensus-state3: consensus-state3(T),
MaName: MaName,
Knd: Knd,
sq_type: SQType(T),
atom: Atom,
atom: Atom$n,
sqequal: s ~ t,
nat_plus: 
,
rationals: 
,
dstype: dstype(TypeNames; d; a),
string: Error :string
Lemmas :
member_singleton,
fpf-domain-join,
product_subtype_base,
list_subtype_base,
int_subtype_base,
decidable__l_member,
decidable__equal_int,
subtype_base_sq,
atom2_subtype_base,
fpf-trivial-subtype-top,
decidable__equal_Id,
cs-precondition_wf,
fpf-join_wf,
fpf-single_wf,
int-deq_wf,
nil_member,
squash_wf,
subtype_rel_function,
subtype_rel_self,
subtype_rel_simple_product,
true_wf,
consensus-state4_wf,
top_wf,
member_wf,
cs-estimate_wf,
fpf-domain_wf,
l_member_wf,
subtype_rel_wf,
cs-inning_wf,
le_wf,
ts-reachable_wf,
consensus-ts4_wf,
ts-type_wf,
Id_wf,
nat_wf,
fpf-domain_wf2,
length_wf1,
select_wf,
intensional-universe_wf,
list-subtype,
fpf-type,
fpf_wf,
subtype-fpf2,
subtype-top,
ts-reachable-induction,
sq_stable_wf,
sq_stable__all,
sq_stable_from_decidable,
decidable__le,
not_wf,
false_wf,
ts-init_wf_reachable,
ts-init_wf,
ts-rel_wf
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[a:\{a:Id| (a \mmember{} A)\} ].
\mforall{}[x:ts-reachable(consensus-ts4(V;A;W))]. \mforall{}[i:\mBbbZ{}].
i \mleq{} Inning(x;a) supposing (i \mmember{} fpf-domain(Estimate(x;a)))
Date html generated:
2011_08_16-AM-09_58_41
Last ObjectModification:
2011_06_18-AM-08_57_11
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