Nuprl Lemma : pv11_p1_unique_adopted
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀accpts,ldrs:bag(Id).
∀ldrs_uid:Id ⟶ ℤ. ∀reps:bag(Id). ∀bnum:pv11_p1_Ballot_Num(). ∀pvals1,pvals2:(pv11_p1_Ballot_Num() × ℤ × Cmd) List.
∀proposals1,proposals2:(ℤ × Cmd) List. ∀b1,b2:𝔹.
(pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ <bnum, pvals1> ∈ pv11_p1_adopted'base(Cmd;f)(e1)
⇒ <bnum, pvals2> ∈ pv11_p1_adopted'base(Cmd;f)(e2)
⇒ <bnum, b1, proposals1> ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e1)
⇒ <bnum, b2, proposals2> ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e2)
⇒ e1 ≤loc e2
⇒ (pvals1 = pvals2 ∈ ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
Proof
Definitions occuring in Statement :
pv11_p1_message-constraint: pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; mf; es),
pv11_p1_LeaderState: pv11_p1_LeaderState(Cmd;ldrs_uid;mf),
pv11_p1_adopted'base: pv11_p1_adopted'base(Cmd;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
bool: 𝔹,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
l_all: (∀x∈L.P[x]),
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
listp: A List+,
name: Name,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
length: ||as||,
list_ind: list_ind,
pv11_p1_headers: pv11_p1_headers(),
cons: [a / b],
nil: [],
it: ⋅,
true: True,
select: L[n],
subtract: n - m,
uimplies: b supposing a,
guard: {T},
rev_implies: P ⇐ Q,
pv11_p1_headers_fun: pv11_p1_headers_fun(Cmd),
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
null: null(as),
es-le: e ≤loc e' ,
or: P ∨ Q,
pv11_p1_adopted'base: pv11_p1_adopted'base(Cmd;mf),
encodes-msg-type: hdr encodes T,
single-valued-classrel: single-valued-classrel(es;X;T),
pi2: snd(t),
pv11_p1_message-constraint: pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; mf; es),
eo-msg-interface-constraint: eo-msg-interface-constraint(es;X;hdrs;f),
uiff: uiff(P;Q),
es-header: header(e),
pv11_p1_headers_no_inputs: pv11_p1_headers_no_inputs(),
top: Top,
exists: ∃x:A. B[x],
make-msg-interface: make-msg-interface(i;l;m),
has-es-info-type: has-es-info-type(es;e;f;T),
es-locl: (e <loc e'),
no-prior-classrel: (no X prior to e),
alle-lt: ∀e<e'.P[e],
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
pv11_p1_p1b'base: pv11_p1_p1b'base(Cmd;mf),
pv11_p1_scout_output: pv11_p1_scout_output(Cmd;accpts;mf),
spreadn: spread4,
pi1: fst(t),
bool: 𝔹,
unit: Unit,
satisfiable_int_formula: satisfiable_int_formula(fmla),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
sq_type: SQType(T),
pv11_p1_init_ballot_num: pv11_p1_init_ballot_num(),
pv11_p1_upd_bnum: pv11_p1_upd_bnum(),
pv11_p1_mk_bnum: pv11_p1_mk_bnum(),
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
isl: isl(x),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_is_bnum: pv11_p1_is_bnum(),
pv11_p1_lt_bnum': pv11_p1_lt_bnum'(ldrs_uid),
es-info-body: msgval(e),
msg-body: msg-body(msg),
outl: outl(x),
outr: outr(x),
assert: ↑b,
pv11_p1_preempted'base: pv11_p1_preempted'base(Cmd;mf),
spreadn: spread3,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
no-classrel-in-interval: (no X between start and e),
msg-header: msg-header(m),
msg-msg: msg-msg(m),
es-info: info(e),
record-select: r.x,
eo-forward: eo.e,
eo-restrict: eo-restrict(eo;P),
record-update: r[x := v],
es-info-type: es-info-type(es;e;f),
msg-type: msg-type(msg;f),
nat: ℕ
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e1,e2:E.
\mforall{}accpts,ldrs:bag(Id). \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}reps:bag(Id). \mforall{}bnum:pv11\_p1\_Ballot\000C\_Num().
\mforall{}pvals1,pvals2:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List. \mforall{}proposals1,proposals2:(\mBbbZ{} \mtimes{} Cmd) List.
\mforall{}b1,b2:\mBbbB{}.
(pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} <bnum, pvals1> \mmember{} pv11\_p1\_adopted'base(Cmd;f)(e1)
{}\mRightarrow{} <bnum, pvals2> \mmember{} pv11\_p1\_adopted'base(Cmd;f)(e2)
{}\mRightarrow{} <bnum, b1, proposals1> \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e1)
{}\mRightarrow{} <bnum, b2, proposals2> \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e2)
{}\mRightarrow{} e1 \mleq{}loc e2
{}\mRightarrow{} (pvals1 = pvals2))
Date html generated:
2016_05_17-PM-03_43_23
Last ObjectModification:
2016_01_18-AM-11_24_55
Theory : paxos!synod
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