Nuprl Lemma : Paxos-spec8-body_wf
[Info:Type]. [es:EO+(Info)]. [failset:Id List]. [T:Type]. [f:
]. [acceptors:Id List]. [Decide,Input:EClass(T)].
[leader: 
Id]. [1a:EClass(Id 
)]. [1b:EClass(Id ( T?))]. [2a:EClass(Id T)]. [2b:EClass(Id
)].
(Paxos-spec8-body{i:l}(es; Info; T; f; acceptors; leader; Input; Decide; 1a; 1b; 2a; 2b; failset) 
')
Proof not projected
Definitions occuring in Statement :
Paxos-spec8-body: Paxos-spec8-body{i:l}(es; Info; T; f; acceptors; leader; Input; Decide; 1a; 1b; 2a; 2b; failset),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
bool: ,
nat: ,
uall: [x:A]. B[x],
prop: ,
unit: Unit,
member: t T,
function: x:A B[x],
product: x:A B[x],
union: left + right,
list: type List,
universe: Type
Definitions :
infix_ap: x f y,
es-causl: (e < e'),
bfalse: ff,
es-collect-filter: Collect(size v's from X with maximum num[v] such that P[v]),
es-interface-pair-prior: X;Y,
eq_int: (i =
j),
mapfilter-class: (f[v] where v from X such that P[v]),
es-class-reply-or-fail: es-class-reply-or-fail,
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),
minus: -n,
es-prior-class-when: (X'?d) when Y,
map-class: (f[v] where v from X),
rev_implies: P 
Q,
iff: P 
Q,
atom: Atom$n,
p-outcome: Outcome,
imax: imax(a;b),
es-interface-accum: es-interface-accum(f;x;X),
le_int: i 
z j,
spread: spread def,
permutation: permutation(T;L1;L2),
quotient: x,y:A//B[x; y],
empty-bag: {},
pair: <a, b>,
single-bag: {x},
lt_int: i <z j,
grp_car: |g|,
real: 
,
rationals: 
,
nat_plus: 
,
es-loc: loc(e),
es-interface-val: val(X,e),
pi2: snd(t),
void: Void,
true: True,
guard: {T},
btrue: tt,
in-eclass: e 
X,
sq_type: SQType(T),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
record-select: r.x,
eclass-val: X(e),
pi1: fst(t),
limited-type: LimitedType,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
deq: EqDecider(T),
id-deq: IdDeq,
deq-member: deq-member(eq;x;L),
filter: filter(P;l),
no_repeats: no_repeats(T;l),
natural_number: $n,
multiply: n * m,
add: n + m,
length: ||as||,
cand: A c
B,
bag: bag(T),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
es-class-mcast-fail: es-class-mcast-fail,
es-locl: (e <loc e'),
top: Top,
assert: 
b,
alle-lt: e<e'.P[e],
spreadn: spread3,
so_lambda: 
x.t[x],
es-collect-opt-max: es-collect-opt-max,
es-filter-image: f[X],
es-E-interface: E(X),
es-le: e loc e' ,
or: P 
Q,
exists: 
x:A. B[x],
apply: f a,
let: let,
subtype: S 
T,
event_ordering: EO,
es-E: E,
lambda: x.A[x],
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
dep-isect: Error :dep-isect,
record+: record+,
ge: i 
j ,
less_than: a < b,
uimplies: b supposing a,
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
implies: P Q,
false: False,
not: 
A,
le: A B,
set: {x:A| B[x]} ,
axiom: Ax,
Paxos-spec8-body: Paxos-spec8-body{i:l}(es; Info; T; f; acceptors; leader; Input; Decide; 1a; 1b; 2a; 2b; failset),
prop: ,
function: x:A B[x],
so_lambda: x y.t[x; y],
equal: s = t,
event-ordering+: EO+(Info),
list: type List,
universe: Type,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
MaAuto: Error :MaAuto,
THENL_cons: Error :THENL_nil,
tactic: Error :tactic,
THENL_cons: Error :THENL_cons,
Complete: Error :Complete,
THENL_v2: Error :THENL,
Repeat: Error :Repeat,
CollapseTHEN: Error :CollapseTHEN,
unit: Unit,
nat: ,
product: x:A B[x],
union: left + right,
Id: Id,
eclass: EClass(A[eo; e]),
int: 
,
bool: ,
RepeatFor: Error :RepeatFor,
Unfold: Error :Unfold,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
Try: Error :Try
Lemmas :
eclass_wf,
member_wf,
nat_wf,
Id_wf,
event-ordering+_wf,
es-E_wf,
bool_wf,
event-ordering+_inc,
unit_wf,
es-le_wf,
es-collect-opt-max_wf,
es-E-interface_wf,
assert_wf,
not_wf,
alle-lt_wf,
es-locl_wf,
es-class-mcast-fail_wf,
length_wf1,
nat_properties,
no_repeats_wf,
le_wf,
filter_wf,
deq-member_wf,
id-deq_wf,
es-interface-top,
pi1_wf_top,
eclass-val_wf,
top_wf,
es-base-E_wf,
subtype_rel_self,
subtype_base_sq,
bool_subtype_base,
assert_elim,
in-eclass_wf,
pi2_wf,
subtype_rel_wf,
false_wf,
ifthenelse_wf,
true_wf,
es-loc_wf,
nat_plus_wf,
es-filter-image_wf,
permutation_wf,
bag_wf,
lt_int_wf,
single-bag_wf,
empty-bag_wf,
le_int_wf,
es-interface-accum_wf,
imax_wf,
imax_ub,
es-prior-class-when_wf,
map-class_wf,
es-interface-subtype_rel2,
es-tagged-true-class_wf,
accum-class_wf,
it_wf,
es-class-reply-or-fail_wf,
pi1_wf,
es-collect-filter_wf,
es-interface-pair-prior_wf,
mapfilter-class_wf,
eq_int_wf,
bfalse_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[failset:Id List]. \mforall{}[T:Type]. \mforall{}[f:\mBbbN{}]. \mforall{}[acceptors:Id List].
\mforall{}[Decide,Input:EClass(T)]. \mforall{}[leader:\mBbbN{} {}\mrightarrow{} Id]. \mforall{}[1a:EClass(Id \mtimes{} \mBbbN{})]. \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{})].
(Paxos-spec8-body\{i:l\}(es; Info; T; f; acceptors; leader; Input; Decide; 1a; 1b; 2a; 2b; failset)
\mmember{} \mBbbP{}')
Date html generated:
2011_10_20-PM-04_46_23
Last ObjectModification:
2011_06_18-PM-02_11_48
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