{ 
es:EO+(Message). failset:Id List. T:LimitedType. f:
.
acceptors,leaders:Id List. Decide,Input:EClass(T).
tg1a,tg1b,tg2a,tg2b,tgpaxos:Id.
(Paxos-spec9-body(es;T;f;acceptors;leaders;...;...;tg1a;...;...;...;...;...)
{i''}) }
{ Proof }
Definitions occuring in Statement :
Paxos-spec9-body: Paxos-spec9-body(es;T;f;acceptors;leaders;Input;Decide;...;...;...;...;...;...),
Message: Message,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
nat: ,
prop: ,
all: x:A. B[x],
member: t T,
list: type List,
limited-type: LimitedType
Definitions :
Auto: Error :Auto,
Unfold: Error :Unfold,
RepeatFor: Error :RepeatFor,
THENL_v2: Error :THENL,
THENL_cons: Error :THENL_cons,
ExRepD: Error :ExRepD,
THENL_cons: Error :THENL_nil,
tactic: Error :tactic,
AssertBY: Error :AssertBY,
subtype_rel: A 
r B,
es-E-interface: E(X),
src-class: Error :src-class,
CollapseTHEN: Error :CollapseTHEN,
THENM: Error :THENM,
CollapseTHENA: Error :CollapseTHENA,
MaAuto: Error :MaAuto,
int: 
,
bool: 
,
es-interface: Temporary AbsInterface(es;A),
union: left + right,
product: x:A 
B[x],
nat: ,
unit: Unit,
Paxos-spec9-body: Paxos-spec9-body(es;T;f;acceptors;leaders;Input;Decide;...;...;...;...;...;...),
deq: EqDecider(T),
cand: A c
B,
nil: [],
exists: 
x:A. B[x],
l_member: (x l),
sqequal: s ~ t,
limited-type: LimitedType,
intensional-universe: IType,
es-is-interface: (e in X),
nat_plus: 
,
isect: 
x:A. B[x],
p-outcome: Outcome,
rationals: 
,
iff: P 
Q,
rev_implies: P Q,
or: P 
Q,
less_than: a < b,
sq_type: SQType(T),
guard: {T},
fpf: a:A fp-> B[a],
top: Top,
ge: i 
j ,
strong-subtype: strong-subtype(A;B),
fpf-cap: f(x)?z,
so_lambda: 
x y.t[x; y],
grp_car: Error :grp_car,
real: 
,
subtype: S T,
let: let,
so_lambda: x.t[x],
void: Void,
false: False,
atom: Atom$n,
accum-class: accum-class(a,x.f[a; x]; x.base[x]; X),
es-tagged-true-class: Tagged_tt(X),
map-class: (f[v] where v from X),
spread: spread def,
es-prior-class-when: (X'?d) when Y,
minus: -n,
es-interface-accum: es-interface-accum(f;x;X),
imax: imax(a;b),
le_int: i 
z j,
es-filter-image: f[X],
spreadn: spread3,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
inl: inl x ,
pair: <a, b>,
inr: inr x ,
it: 
,
es-collect-opt-max: es-collect-opt-max,
pi1: fst(t),
pi2: snd(t),
es-in-ports: Error :es-in-ports,
prop: ,
add: n + m,
multiply: n * m,
natural_number: $n,
no_repeats: no_repeats(T;l),
le: A B,
length: ||as||,
filter: filter(P;l),
lambda: x.A[x],
deq-member: deq-member(eq;x;L),
id-deq: IdDeq,
and: P Q,
l_all: (xL.P[x]),
all: x:A. B[x],
es-E: E,
implies: P Q,
function: x:A 
B[x],
es-kind: Error :es-kind,
es-valtype: Error :es-valtype,
not: 
A,
set: {x:A| B[x]} ,
Knd: Knd,
assert: 
b,
isrcv: isrcv(k),
rcvs-on: Rcvs(tg) on links,
links-from-to: links(tg) from srclocs to dstlocs,
Id: Id,
list: type List,
equal: s = t,
event_ordering: EO,
member: t T,
universe: Type,
ORELSE: Error :ORELSE,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
bor: p 
q,
bimplies: p q,
es-eq-E: e = e',
eq_pcl_key: Error :eq_pcl_key,
pcl-key-contains: Error :pcl-key-contains,
eq_pcl_basic: Error :eq_pcl_basic,
eq_pcl_term: Error :eq_pcl_term,
IdLnk: IdLnk,
isrcvl: isrcvl(l;k),
can-apply: can-apply(f;x),
isl: isl(x),
es-loc: loc(e),
fset: fset(T),
b-union: A 
B,
fpf-sub: f g,
partitions: partitions(I;p),
i-member: r I,
rleq: x y,
rnonneg: rnonneg(r),
req: x = y,
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
prime_ideal_p: Error :prime_ideal_p,
integ_dom_p: Error :integ_dom_p,
grp_leq: Error :grp_leq,
monoid_hom_p: Error :monoid_hom_p,
group_p: Error :group_p,
monoid_p: Error :monoid_p,
monot: Error :monot,
cancel: Error :cancel,
fun_thru_2op: Error :fun_thru_2op,
fun_thru_1op: Error :fun_thru_1op,
dist_1op_2op_lr: Error :dist_1op_2op_lr,
action_p: Error :action_p,
bilinear_p: Error :bilinear_p,
bilinear: Error :bilinear,
inverse: Error :inverse,
comm: Error :comm,
assoc: Error :assoc,
ident: Error :ident,
coprime: CoPrime(a,b),
connex: Connex(T;x,y.R[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
eqfun_p: IsEqFun(T;eq),
inv_funs: InvFuns(A;B;f;g),
uni_sat: a = !x:T. Q[x],
sq_stable: SqStable(P),
f2f+-pred: Error :f2f+-pred,
rcv-it: Error :rcv-it,
snd-it: Error :snd-it,
same-thread: same-thread(es;p;e;e'),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
ses-legal-sequence: Legal(pas) given prvt,
ses-action: Action(e),
path-goes-thru: x-f*-y thru i,
cut-order: a (X;f) b,
es-fset-loc: i locs(s),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
existse-between3: e(e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
alle-between2: e[e1,e2].P[e],
existse-between1: e[e1,e2).P[e],
alle-between1: e[e1,e2).P[e],
alle-le: ee'.P[e],
alle-lt: e<e'.P[e],
existse-le: ee'.P[e],
existse-before: e<e'.P[e],
es-causle: e c e',
es-causl: (e < e'),
es-le: e loc e' ,
es-locl: (e <loc e'),
cs-precondition: state s may consider v in inning i,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
fset-closed: (s closed under fs),
f-subset: xs ys,
fset-member: a s,
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
fun-connected: y is f*(x),
l_disjoint: l_disjoint(T;l1;l2),
prime: prime(a),
reducible: reducible(a),
inject: Inj(A;B;f),
l_contains: A B,
l_exists: (xL. P[x]),
infix_ap: x f y,
apply: f a,
grp_lt: Error :grp_lt,
set_lt: Error :set_lt,
set_leq: Error :set_leq,
assoced: a ~ b,
divides: b | a,
decidable: Dec(P),
squash: 
T,
rcv-class: Error :rcv-class,
imax-class: (maximum f[v] lb with v from X),
es-interface-at: X@i,
es-isrcv: Error :es-isrcv,
bfalse: ff,
bnot: b,
es-filtered-propagation: Error :es-filtered-propagation,
surject: Surj(A;B;f),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
btrue: tt,
band: p q,
eq_id: a = b,
ldst: destination(l),
lsrc: source(l),
lnk: lnk(k),
es-filtered-propagate-iff1: Error :es-filtered-propagate-iff1,
fpf-dom: x dom(f),
eq_knd: a = b,
locl: locl(a),
append: as @ bs,
so_apply: x[s],
class-program: ClassProgram(T),
ma-state: State(ds),
decl-state: Error :decl-state,
es-state: Error :es-state,
es-vartype: Error :es-vartype,
sum: 
(f[x] | x < k),
sum-map: f[x] for x L,
hd: hd(l),
tl: tl(l),
es-interface-val: val(X,e),
rel_plus: R,
cless: Error :cless,
mapfilter-class: (f[v] where v from X such that P[v]),
eq_int: (i =
j),
es-interface-pair-prior: X;Y,
es-collect-filter: Collect(size v's from X with maximum num[v] such that P[v]),
es-propagate-iff1: X Y:T,
cons: [car / cdr],
consensus-rcv: consensus-rcv(V;A),
consensus-state3: consensus-state3(T),
MaName: MaName,
select: l[i],
remove-repeats: remove-repeats(eq;L),
last: last(L),
map: map(f;as)
Lemmas :
l_member-settype,
decidable__equal_Kind,
decidable__l_member,
es-loc_wf,
es-le_wf,
alle-lt_wf,
bfalse_wf,
es-interface-val_wf2,
es-locl_wf,
es-interface-at_wf,
es-propagate-iff1_wf,
l_all_wf,
nat_plus_wf,
es-collect-filter_wf,
es-interface-pair-prior_wf,
eq_int_wf,
mapfilter-class_wf,
assert-eq-knd,
member_singleton,
assert_elim,
bool_sq,
Error :is-src,
Knd_sq,
E-prior-class-when,
E-map-class,
rev_implies_wf,
iff_wf,
decidable__assert,
sq_stable_from_decidable,
es-E-interface-property,
member-interface-at,
lnk_wf,
IdLnk_wf,
lsrc_wf,
ldst_wf,
eq_id_wf,
bnot_wf,
assert-eq-id,
not_functionality_wrt_iff,
assert_of_bnot,
iff_transitivity,
eqff_to_assert,
eqtt_to_assert,
band_wf,
Error :es-filtered-propagate-iff1_wf,
surject_wf,
Error :es-filtered-propagation_wf,
unit_wf,
nat_wf,
es-interface_wf,
it_wf,
map-class_wf,
es-prior-class-when_wf,
member_wf,
pi1_wf,
lt_int_wf,
ifthenelse_wf,
accum-class_wf,
es-tagged-true-class_wf,
bool_wf,
le_wf,
subtype_rel_wf,
length_wf_nat,
es-interface-subtype_rel,
top_wf,
es-interface-top,
le_int_wf,
nat_properties,
imax_ub,
imax_wf,
es-interface-accum_wf,
es-filter-image_wf,
pi2_wf,
es-collect-opt-max_wf,
Error :src-class_wf,
es-is-interface_wf,
Id_wf,
assert_wf,
es-E-interface_wf,
intensional-universe_wf,
Error :in-ports-src-class,
guard_wf,
Error :es-kind_wf,
l_member_wf,
Knd_wf,
Error :es-valtype_wf,
es-E_wf,
Error :es-in-ports_wf,
isrcv_wf,
not_wf,
l_all_wf2,
id-deq_wf,
deq-member_wf,
filter_wf,
length_wf1,
no_repeats_wf,
rcvs-on_wf,
links-from-to_wf,
event_ordering_wf
\mforall{}es:EO+(Message). \mforall{}failset:Id List. \mforall{}T:LimitedType. \mforall{}f:\mBbbN{}. \mforall{}acceptors,leaders:Id List.
\mforall{}Decide,Input:EClass(T). \mforall{}tg1a,tg1b,tg2a,tg2b,tgpaxos:Id.
(Paxos-spec9-body(es;T;f;acceptors;leaders;Input;Decide;tg1a;tg1b;tg2a;tg2b;tgpaxos;failset)
\mmember{} \mBbbP{}\{i''\})
Date html generated:
2010_08_30-AM-01_01_39
Last ObjectModification:
2010_08_21-PM-09_49_00
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