Nuprl Lemma : Paxos-partial-spec8-locations
[Info:Type]. [es:EO+(Info)]. [T:Type]. [leader:
Id]. [failset:Id List]. [1a:EClass(Id 
)].
[Decide,Input:EClass(T)]. [f:
]. [acceptors:Id List]. [1b:EClass(Id ( T?))]. [2a:EClass(Id T)].
[2b:EClass(Id 
)].
([e:E(1a)]. ((fst(1a(e))) = (leader (snd(1a(e))))))
([e:E(1b)]. (loc(e) = (leader (fst(snd(1b(e)))))))
([e:E(2a)]. ((fst(2a(e))) = (leader (fst(snd(2a(e)))))))
([e:E(2b)]. (loc(e) = (leader (fst(snd(2b(e)))))))
supposing Paxos-partial-spec8{i:l}(Info; es; T; f; acceptors; leader; Input; Decide; 1a; 1b; 2a; 2b; failset)
Proof not projected
Definitions occuring in Statement :
Paxos-partial-spec8: Paxos-partial-spec8{i:l}(Info; es; T; f; acceptors; leader; Input; Decide; 1a; 1b; 2a; 2b; failset),
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
Id: Id,
bool: ,
nat_plus: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
and: P Q,
unit: Unit,
apply: f a,
function: x:A B[x],
product: x:A B[x],
union: left + right,
list: type List,
universe: Type,
equal: s = t
Definitions :
es-class-reply-or-fail: es-class-reply-or-fail,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
es-class-mcast-fail: es-class-mcast-fail,
exists: 
x:A. B[x],
it: 
,
inr: inr x ,
inl: inl x ,
accum-class: accum-class(a,x.f[a; x];x.base[x];X),
es-tagged-true-class: Tagged_tt(X),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: 
b,
guard: {T},
sq_type: SQType(T),
minus: -n,
es-prior-class-when: (X'?d) when Y,
le_int: i 
z j,
map-class: (f[v] where v from X),
rev_implies: P 
Q,
iff: P 
Q,
or: P 
Q,
multiply: n * m,
grp_car: |g|,
atom: Atom$n,
p-outcome: Outcome,
false: False,
imax: imax(a;b),
es-interface-accum: es-interface-accum(f;x;X),
spread: spread def,
permutation: permutation(T;L1;L2),
quotient: x,y:A//B[x; y],
empty-bag: {},
single-bag: {x},
lt_int: i <z j,
spreadn: spread3,
es-filter-image: f[X],
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
bag: bag(T),
int_nzero: 
,
void: Void,
length: ||as||,
real: 
,
rationals: 
,
so_lambda: 
x.t[x],
natural_number: $n,
add: n + m,
es-collect-opt-max: es-collect-opt-max,
implies: P Q,
event_ordering: EO,
es-E: E,
lambda: x.A[x],
subtype: S 
T,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
let: let,
dep-isect: Error :dep-isect,
record+: record+,
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A r B,
set: {x:A| B[x]} ,
all: x:A. B[x],
es-loc: loc(e),
axiom: Ax,
pi2: snd(t),
apply: f a,
eclass-val: X(e),
pi1: fst(t),
top: Top,
es-E-interface: E(X),
pair: <a, b>,
prop: 
,
Paxos-partial-spec8: Paxos-partial-spec8{i:l}(Info; es; T; f; acceptors; leader; Input; Decide; 1a; 1b; 2a; 2b; failset),
nat_plus: ,
so_lambda: x y.t[x; y],
list: type List,
uimplies: b supposing a,
and: P Q,
equal: s = t,
event-ordering+: EO+(Info),
universe: Type,
uall: [x:A]. B[x],
function: x:A B[x],
member: t 
T,
isect: 
x:A. B[x],
D: Error :D,
unit: Unit,
nat: ,
product: x:A B[x],
union: left + right,
Id: Id,
eclass: EClass(A[eo; e]),
CollapseTHEN: Error :CollapseTHEN,
int: ,
bool: ,
MaAuto: Error :MaAuto,
CollapseTHENA: Error :CollapseTHENA,
Try: Error :Try,
Complete: Error :Complete,
Auto: Error :Auto,
cand: A c B,
btrue: tt,
in-eclass: e 
X,
true: True,
squash: 
T,
es-causle: e c e',
l_member: (x l),
limited-type: LimitedType,
sqequal: s ~ t,
l_all: (xL.P[x]),
ExRepD: Error :ExRepD,
ParallelOp: Error :ParallelOp,
RepeatFor: Error :RepeatFor,
BHyp: Error :BHyp,
es-prior-val: (X)',
es-prior-interface: prior(X),
es-interface-at: X@i,
intensional-universe: IType,
tag-by: zT,
ldag: LabeledDAG(T),
labeled-graph: LabeledGraph(T),
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 T2,
b-union: A 
B,
fpf-cap: f(x)?z,
record: record(x.T[x]),
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),
fpf-dom: x dom(f),
infix_ap: x f y,
es-causl: (e < e'),
tactic: Error :tactic,
ext-eq: A 
B,
rev_subtype_rel: A 
r B,
rev_uimplies: rev_uimplies(P;Q),
eclass-compose1: f o X,
so_apply: x[s],
ma-state: State(ds),
es-interface-part: (X|g=i),
class-program: ClassProgram(T),
es-empty-interface: Empty,
cond-class: [X?Y],
base: Base,
imax-class: (maximum f[v] lb with v from X),
es-interface-val: val(X,e),
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
bfalse: ff,
eq_int: (i =
j),
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'),
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_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p q,
band: p q,
bor: p q,
bnot: b,
bag-only: only(bs),
bag-size: bag-size(bs),
es-interface-predecessors: (X)(e),
filter: filter(P;l),
alle-lt: e<e'.P[e],
es-first-at: e is first@ i s.t. e.P[e],
outl: outl(x),
isl: isl(x),
list-max: list-max(x.f[x];L),
skip: Error :skip,
HypSubst: Error :HypSubst
Lemmas :
map-class-val,
is-map-class,
collect-opt-max-val,
rev_implies_wf,
iff_wf,
es-interface-predecessors_wf,
filter_wf,
list-max_wf,
outl_wf,
is-collect-opt-max,
assert_functionality_wrt_uiff,
eqff_to_assert,
uiff_transitivity,
assert_of_lt_int,
eqtt_to_assert,
es-filter-image-val,
es-is-filter-image,
bnot_of_lt_int,
assert_of_le_int,
bnot_wf,
member-interface-at,
es-interface-at_wf,
es-interface-val_wf2,
squash_wf,
es-E-filter-image,
ext-eq_inversion,
subtype_rel_functionality_wrt_implies,
subtype_rel_weakening,
ext-eq_weakening,
true_wf,
is-prior-class-when,
prior-class-when-val,
sq_stable__assert,
intensional-universe_wf,
product_subtype_base,
unit_subtype_base,
union_subtype_base,
pi1_wf,
atom2_subtype_base,
set_subtype_base,
int_subtype_base,
assert_wf,
subtype_base_sq,
bool_subtype_base,
assert_elim,
in-eclass_wf,
es-loc_wf,
eclass-val_wf,
Paxos-partial-spec8_wf,
eclass_wf,
Id_wf,
nat_plus_wf,
es-E-interface_wf,
nat_wf,
event-ordering+_wf,
member_wf,
subtype_rel_wf,
es-interface-top,
unit_wf,
bool_wf,
nat_plus_inc,
es-E_wf,
event-ordering+_inc,
es-collect-opt-max_wf,
pi1_wf_top,
pi2_wf,
top_wf,
es-base-E_wf,
subtype_rel_self,
es-filter-image_wf,
permutation_wf,
bag_wf,
ifthenelse_wf,
lt_int_wf,
nat_properties,
single-bag_wf,
empty-bag_wf,
es-interface-accum_wf,
le_wf,
not_wf,
false_wf,
imax_wf,
imax_ub,
es-prior-class-when_wf,
map-class_wf,
le_int_wf,
es-interface-subtype_rel2,
es-tagged-true-class_wf,
accum-class_wf,
it_wf,
uall_wf,
es-class-mcast-fail_wf,
es-class-reply-or-fail_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[leader:\mBbbN{} {}\mrightarrow{} Id]. \mforall{}[failset:Id List].
\mforall{}[1a:EClass(Id \mtimes{} \mBbbN{})]. \mforall{}[Decide,Input:EClass(T)]. \mforall{}[f:\mBbbN{}\msupplus{}]. \mforall{}[acceptors:Id List]. \mforall{}[1b:EClass(Id
\mtimes{} \mBbbN{}
\mtimes{} (\mBbbN{} \mtimes{} T?))].
\mforall{}[2a:EClass(Id \mtimes{} \mBbbN{} \mtimes{} T)]. \mforall{}[2b:EClass(Id \mtimes{} \mBbbN{} \mtimes{} \mBbbB{})].
(\mforall{}[e:E(1a)]. ((fst(1a(e))) = (leader (snd(1a(e))))))
\mwedge{} (\mforall{}[e:E(1b)]. (loc(e) = (leader (fst(snd(1b(e)))))))
\mwedge{} (\mforall{}[e:E(2a)]. ((fst(2a(e))) = (leader (fst(snd(2a(e)))))))
\mwedge{} (\mforall{}[e:E(2b)]. (loc(e) = (leader (fst(snd(2b(e)))))))
supposing Paxos-partial-spec8\{i:l\}(Info;
es;
T;
f;
acceptors;
leader;
Input;
Decide;
1a;
1b;
2a;
2b;
failset)
Date html generated:
2011_10_20-PM-04_47_51
Last ObjectModification:
2011_06_18-PM-02_14_11
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