{ 
[V:Type]
((v,v':V. Dec(v = v'))
(A:Id List. W:{a:Id| (a 
A)} List List.
x,y:ts-reachable(consensus-ts4(V;A;W)). i:
. v:V.
((x ts-rel(consensus-ts4(V;A;W)) y)
in state y, inning i could commit v
in state x, inning i could commit v ))) }
{ Proof }
Definitions occuring in Statement :
cs-inning-committable: in state s, inning i could commit v ,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
nat: ,
decidable: Dec(P),
uall: [x:A]. B[x],
infix_ap: x f y,
all: x:A. B[x],
implies: P Q,
set: {x:A| B[x]} ,
list: type List,
universe: Type,
equal: s = t,
l_member: (x l),
ts-reachable: ts-reachable(ts),
ts-rel: ts-rel(ts)
Definitions :
rel_star: R^*,
spread: spread def,
pi1: fst(t),
limited-type: LimitedType,
fpf: a:A fp-> B[a],
ts-type: ts-type(ts),
real: 
,
grp_car: |g|,
subtype: S 
T,
member: t T,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A r B,
consensus-state4: ConsensusState,
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
union: left + right,
or: P 
Q,
and: P 
Q,
false: False,
not: 
A,
le: A 
B,
int: 
,
ts-rel: ts-rel(ts),
apply: f a,
infix_ap: x f y,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
cs-inning-committable: in state s, inning i could commit v ,
exists: 
x:A. B[x],
product: x:A 
B[x],
universe: Type,
implies: P Q,
decidable: Dec(P),
equal: s = t,
prop: 
,
list: type List,
set: {x:A| B[x]} ,
l_member: (x l),
Id: Id,
ts-reachable: ts-reachable(ts),
consensus-ts4: consensus-ts4(V;A;W),
all: x:A. B[x],
function: x:A 
B[x],
nat: ,
Auto: Error :Auto,
Complete: Error :Complete,
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
tactic: Error :tactic,
so_lambda: 
x.t[x],
CollapseTHENA: Error :CollapseTHENA,
D: Error :D,
cs-inning: Inning(s;a),
cs-estimate: Estimate(s;a),
fpf-domain: fpf-domain(f),
AssertBY: Error :AssertBY,
consensus-rel: CR[x,y],
lambda: x.A[x],
cand: A c B,
fpf-single: x : v,
int-deq: IntDeq,
fpf-join: f 
g,
cs-precondition: state s may consider v in inning i,
natural_number: $n,
add: n + m,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
pair: <a, b>,
bool: 
,
void: Void,
guard: {T},
fpf-ap: f(x),
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
l_disjoint: l_disjoint(T;l1;l2),
consensus-state3: consensus-state3(T),
sq_type: SQType(T),
atom: Atom,
atom: Atom$n,
rev_implies: P 
Q,
iff: P Q,
eqof: eqof(d),
intensional-universe: IType,
list_ind: list_ind def,
reduce: reduce(f;k;as),
deq-member: deq-member(eq;x;L),
deq: EqDecider(T),
true: True,
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 ,
assert: 
b,
top: Top,
fpf-cap: f(x)?z,
squash: 
T,
bag: bag(T),
fpf-sub: f g,
ma-state: State(ds),
rcv: rcv(l,tg),
locl: locl(a),
tag-by: zT,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
b-union: A 
B,
sqequal: s ~ t,
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,
append: as @ bs,
map: map(f;as),
cons: [car / cdr],
hd: hd(l),
last: last(L),
remove-repeats: remove-repeats(eq;L),
select: l[i],
filter: filter(P;l),
length: ||as||,
nil: [],
ts-stable-rel: ts-stable-rel(ts;x,y.R[x; y])
Lemmas :
consensus-ts4-estimate-rel,
rel_rel_star,
consensus-rel_wf,
rel_star_wf,
consensus-ts4-inning-rel,
member_singleton,
not_functionality_wrt_iff,
length_wf1,
select_wf,
list-subtype,
member-fpf-domain,
fpf-domain_wf2,
l_member-settype,
l_member_subtype,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
bool_wf,
iff_weakening_uiff,
bool_subtype_base,
eqtt_to_assert,
bool_cases,
bnot_wf,
fpf-join-ap-sq,
subtype_rel_function,
subtype_rel_self,
subtype_rel_simple_product,
squash_wf,
product_subtype_base,
list_subtype_base,
int_subtype_base,
fpf-domain-join,
fpf-type,
cs-estimate_wf,
subtype-fpf2,
subtype-top,
fpf-single_wf,
assert_wf,
fpf-ap_wf,
intensional-universe_wf,
cs-inning_wf,
int-deq_wf,
fpf_wf,
top_wf,
fpf-domain_wf,
true_wf,
fpf-dom_wf,
ifthenelse_wf,
false_wf,
fpf-trivial-subtype-top,
member-fpf-dom,
subtype_base_sq,
atom2_subtype_base,
decidable__equal_Id,
decidable__cs-not-completed,
not_wf,
nat_properties,
decidable__cs-archived,
cs-not-completed_wf,
le_wf,
uall_wf,
consensus-ts4-estimate-domain,
consensus-ts4_wf,
subtype_rel_wf,
ts-type_wf,
ts-reachable_wf,
nat_wf,
member_wf,
ts-rel_wf,
consensus-state4_wf,
cs-inning-committable_wf,
cs-archived_wf,
Id_wf,
l_member_wf,
decidable_wf
\mforall{}[V:Type]
((\mforall{}v,v':V. Dec(v = v'))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}x,y:ts-reachable(consensus-ts4(V;A;W)). \mforall{}i:\mBbbN{}. \mforall{}v:V\000C.
((x ts-rel(consensus-ts4(V;A;W)) y)
{}\mRightarrow{} in state y, inning i could commit v
{}\mRightarrow{} in state x, inning i could commit v )))
Date html generated:
2011_08_16-AM-10_04_44
Last ObjectModification:
2011_06_18-AM-09_00_59
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