Nuprl Lemma : Paxos-spec6-NewBallot-invariant
[Info:Type]. [es:EO+(Info)]. [failset:Id List]. [T:Type]. [f:
]. [acceptors:Id List].
[Reserve,NoProposal,NewBallot:EClass()]. [VoteState:EClass(AcceptorState)]. [Proposal:EClass( 
T)].
[AcceptOrReject:EClass( T 
)]. [leader: 
Id]. [Decide,Input:EClass(T)]. [Vote:EClass(Id )].
[Collect:EClass( 
T)].
[nb1,nb2:E(NewBallot)]. nb1 = nb2 supposing NewBallot(nb1) = NewBallot(nb2)
supposing Paxos-spec6-body{i:l}(Info;es;T;f;acceptors;
Reserve;VoteState;Proposal;
AcceptOrReject;leader;Decide;
Vote;Input;Collect;NoProposal;
NewBallot;failset)
Proof not projected
Definitions occuring in Statement :
Paxos-spec6-body: Paxos-spec6-body,
paxos-acceptor-state: AcceptorState,
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
bool: ,
nat_plus: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
function: x:A B[x],
product: x:A B[x],
list: type List,
int: ,
universe: Type,
equal: s = t
Definitions :
multiply: n * m,
add: n + m,
lt_int: i <z j,
it: 
,
inr: inr x ,
inl: inl x ,
le_int: i 
z j,
spreadn: spread3,
es-filter-image: f[X],
es-loc: loc(e),
length: ||as||,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
uiff: uiff(P;Q),
axiom: Ax,
true: True,
guard: {T},
btrue: tt,
sq_type: SQType(T),
isl: isl(x),
can-apply: can-apply(f;x),
in-eclass: e 
X,
grp_car: |g|,
eclass-val: X(e),
limited-type: LimitedType,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
l_member: (x l),
alle-lt: e<e'.P[e],
es-le: e loc e' ,
pair: <a, b>,
or: P 
Q,
exists: 
x:A. B[x],
rev_implies: P 
Q,
iff: P 
Q,
es-class-causal-mrel-fail: es-class-causal-mrel-fail,
es-class-def: es-class-def,
es-class-causal-rel-fail: es-class-causal-rel-fail,
no_repeats: no_repeats(T;l),
and: P 
Q,
assert: 
b,
es-E-interface: E(X),
natural_number: $n,
void: Void,
implies: P Q,
false: False,
not: 
A,
le: A B,
real: 
,
rationals: 
,
less_than: a < b,
prop: 
,
Paxos-spec6-body: Paxos-spec6-body,
uimplies: b supposing a,
int: ,
bool: ,
product: x:A B[x],
paxos-acceptor-state: AcceptorState,
union: left + right,
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
top: Top,
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
nat: ,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
set: {x:A| B[x]} ,
nat_plus: ,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
all: x:A. B[x],
function: x:A B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
list: type List,
Id: Id,
universe: Type,
member: t T,
equal: s = t,
event-ordering+: EO+(Info),
tactic: Error :tactic,
proper-iseg: L1 < L2,
iseg: l1 l2,
gt: i > j,
infix_ap: x f y,
es-causl: (e < e'),
es-locl: (e <loc e'),
IdLnk: IdLnk,
append: as @ bs,
locl: locl(a),
Knd: Knd,
so_apply: x[s],
so_apply: x[s1;s2],
so_lambda: x.t[x],
sqequal: s ~ t,
squash: 
T,
MaAuto: Error :MaAuto,
AssertBY: Error :AssertBY,
CollapseTHEN: Error :CollapseTHEN,
Complete: Error :Complete,
ORELSE: Error :ORELSE,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA
Lemmas :
squash_wf,
set_subtype_base,
not_wf,
true_wf,
ifthenelse_wf,
false_wf,
uiff_inversion,
es-locl-total,
es-locl_wf,
es-causl_wf,
eclass_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-E_wf,
Id_wf,
nat_wf,
bool_wf,
paxos-acceptor-state_wf,
nat_plus_wf,
Paxos-spec6-body_wf,
nat_plus_properties,
le_wf,
nat_plus_inc,
es-E-interface_wf,
member_wf,
es-interface-top,
eclass-val_wf,
assert_wf,
subtype_base_sq,
bool_subtype_base,
assert_elim,
in-eclass_wf,
subtype_rel_wf,
length_wf_nat
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[failset:Id List]. \mforall{}[T:Type]. \mforall{}[f:\mBbbN{}\msupplus{}]. \mforall{}[acceptors:Id List].
\mforall{}[Reserve,NoProposal,NewBallot:EClass(\mBbbN{})]. \mforall{}[VoteState:EClass(AcceptorState)].
\mforall{}[Proposal:EClass(\mBbbN{} \mtimes{} T)]. \mforall{}[AcceptOrReject:EClass(\mBbbN{} \mtimes{} T \mtimes{} \mBbbB{})]. \mforall{}[leader:\mBbbN{} {}\mrightarrow{} Id].
\mforall{}[Decide,Input:EClass(T)]. \mforall{}[Vote:EClass(Id \mtimes{} \mBbbN{} \mtimes{} \mBbbB{})]. \mforall{}[Collect:EClass(\mBbbN{} \mtimes{} \mBbbZ{} \mtimes{} T)].
\mforall{}[nb1,nb2:E(NewBallot)]. nb1 = nb2 supposing NewBallot(nb1) = NewBallot(nb2)
supposing Paxos-spec6-body\{i:l\}(Info;es;T;f;acceptors;
Reserve;VoteState;Proposal;
AcceptOrReject;leader;Decide;
Vote;Input;Collect;NoProposal;
NewBallot;failset)
Date html generated:
2011_10_20-PM-04_39_15
Last ObjectModification:
2011_06_18-PM-02_03_53
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