{ 
[V:Type]
[A:Id List]. [W:{a:Id| (a 
A)} List List].
[x:ts-reachable(consensus-ts4(V;A;W))]. [i:
]. [v:V].
[a:{a:Id| (a A)} ].
[j:
i]. [v':V]. v' = v supposing in state x, inning j could commit v'
supposing by state x, a archived v in inning i
supposing v1,v2:V. Dec(v1 = v2) }
{ Proof }
Definitions occuring in Statement :
cs-inning-committable: in state s, inning i could commit v ,
cs-archived: by state s, a archived v in inning i,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
int_seg: {i..j
},
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
set: {x:A| B[x]} ,
list: type List,
natural_number: $n,
int: ,
universe: Type,
equal: s = t,
l_member: (x l),
ts-reachable: ts-reachable(ts)
Definitions :
ts-init: ts-init(ts),
fpf-single: x : v,
cs-inning: Inning(s;a),
consensus-rel: CR[x,y],
fpf-empty: 
,
minus: -n,
lambda: 
x.A[x],
cs-not-completed: in state s, a has not completed inning i,
so_apply: x[s],
guard: {T},
assert: 
b,
natural_number: $n,
real: 
,
rationals: 
,
subtype: S 
T,
pair: <a, b>,
false: False,
lelt: i 
j < k,
axiom: Ax,
cs-inning-committable: in state s, inning i could commit v ,
int_seg: {i..j},
ts-rel: ts-rel(ts),
rel_star: R^*,
so_lambda: 
x.t[x],
tag-by: z
T,
rev_implies: P 
Q,
implies: P 
Q,
iff: P Q,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 
T2,
b-union: A 
B,
true: True,
fpf-cap: f(x)?z,
spread: spread def,
pi1: fst(t),
intensional-universe: IType,
fpf-ap: f(x),
top: Top,
cs-estimate: Estimate(s;a),
fpf-domain: fpf-domain(f),
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
fpf: a:A fp-> B[a],
product: x:A B[x],
exists: 
x:A. B[x],
apply: f a,
infix_ap: x f y,
consensus-state4: ConsensusState,
cs-archived: by state s, a archived v in inning i,
int: ,
transition-system: transition-system{i:l},
ts-type: ts-type(ts),
subtype_rel: A r B,
consensus-ts4: consensus-ts4(V;A;W),
ts-reachable: ts-reachable(ts),
l_member: (x l),
set: {x:A| B[x]} ,
not: 
A,
union: left + right,
or: P 
Q,
bool: 
,
Id: Id,
list: type List,
limited-type: LimitedType,
isect: x:A. B[x],
uall: [x:A]. B[x],
uimplies: b supposing a,
decidable: Dec(P),
prop: 
,
function: x:A 
B[x],
equal: s = t,
universe: Type,
member: t T,
all: x:A. B[x],
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
cand: A c B,
nat: ,
pi2: snd(t),
cons: [car / cdr],
void: Void,
int-deq: IntDeq,
nil: [],
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),
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),
it: 
,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
add: n + m,
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
l_disjoint: l_disjoint(T;l1;l2),
consensus-state3: consensus-state3(T),
atom: Atom,
sq_type: SQType(T),
sqequal: s ~ t,
atom: Atom$n,
fpf-join: f 
g,
eqof: eqof(d),
list_ind: list_ind def,
reduce: reduce(f;k;as),
deq-member: deq-member(eq;x;L),
deq: EqDecider(T),
fpf-dom: x dom(f),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
filter: filter(P;l),
grp_car: |g|,
select: l[i],
length: ||as||,
bag: bag(T),
ma-state: State(ds),
rcv: rcv(l,tg),
locl: locl(a),
bfalse: ff,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
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-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,
bnot: b,
btrue: tt,
MaAuto: Error :MaAuto,
Auto: Error :Auto,
HypSubst: Error :HypSubst,
AssertBY: Error :AssertBY,
D: Error :D,
nequal: a 
b T ,
qless: r < s,
eq_knd: a = b,
quotient: x,y:A//B[x; y],
divides: b | a,
assoced: a ~ b,
set_car: |p|,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
rng_car: |r|,
unit: Unit,
nat_plus: 
,
dstype: dstype(TypeNames; d; a),
string: Error :string,
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,
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)
Lemmas :
decidable__cand,
decidable__equal_int,
decidable__not,
decidable__l_member,
product_subtype_base,
list_subtype_base,
cs-archive-blocked_wf,
cs-precondition_wf,
int_subtype_base,
fpf-join_wf,
member_singleton,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
bool_wf,
not_wf,
iff_weakening_uiff,
bool_subtype_base,
eqtt_to_assert,
bool_cases,
subtype_rel_function,
subtype_rel_self,
subtype_rel_simple_product,
bnot_wf,
not_functionality_wrt_iff,
length_wf1,
select_wf,
list-subtype,
fpf-domain-join,
fpf-single_wf,
fpf-join-ap-sq,
member-fpf-domain,
fpf-type,
subtype-fpf2,
subtype-top,
cs-inning_wf,
assert_wf,
int-deq_wf,
fpf-ap_wf,
fpf-dom_wf,
ifthenelse_wf,
false_wf,
fpf-trivial-subtype-top,
member-fpf-dom,
true_wf,
atom2_subtype_base,
set_subtype_base,
subtype_base_sq,
nat_wf,
decidable__equal_Id,
consensus-rel_wf,
cs-inning-committable-step,
le_wf,
cs-not-completed_wf,
decidable__cs-archived,
ts-reachable-induction,
sq_stable_wf,
sq_stable__all,
sq_stable__uall,
squash_wf,
sq_stable__equal,
ts-init_wf_reachable,
ts-init_wf,
nil_member,
fpf-empty_wf,
pi2_wf,
fpf-domain_wf2,
consensus-state4_wf,
top_wf,
subtype_rel_wf,
ts-reachable_wf,
consensus-ts4_wf,
member_wf,
cs-estimate_wf,
fpf-domain_wf,
l_member_wf,
cs-archived_wf,
Id_wf,
ts-type_wf,
decidable_wf,
intensional-universe_wf,
fpf_wf,
ts-rel_wf,
rel_star_wf,
int_seg_wf,
cs-inning-committable_wf,
uall_wf,
uiff_inversion,
int_seg_properties
\mforall{}[V:Type]
\mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[x:ts-reachable(consensus-ts4(V;A;W))]. \mforall{}[i:\mBbbZ{}].
\mforall{}[v:V]. \mforall{}[a:\{a:Id| (a \mmember{} A)\} ].
\mforall{}[j:\mBbbN{}i]. \mforall{}[v':V]. v' = v supposing in state x, inning j could commit v'
supposing by state x, a archived v in inning i
supposing \mforall{}v1,v2:V. Dec(v1 = v2)
Date html generated:
2011_08_16-AM-10_05_18
Last ObjectModification:
2011_06_18-AM-09_01_07
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