Nuprl Lemma : pv11_p1_unique_adopted_fun
∀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.
(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 = (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e1))) ∈ pv11_p1_Ballot_Num())
⇒ (bnum = (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e2))) ∈ pv11_p1_Ballot_Num())
⇒ 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_LeaderStateFun: pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e),
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,
pi1: fst(t),
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,
pv11_p1_headers: pv11_p1_headers(),
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
uimplies: b supposing a,
pv11_p1_headers_fun: pv11_p1_headers_fun(Cmd),
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
list_ind: list_ind,
cons: [a / b],
band: p ∧b q,
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
nil: [],
it: ⋅,
null: null(as),
top: Top,
pi2: snd(t),
pi1: fst(t)
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.
(pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} <bnum, pvals1> \mmember{} pv11\_p1\_adopted'base(Cmd;f)(e1)
{}\mRightarrow{} <bnum, pvals2> \mmember{} pv11\_p1\_adopted'base(Cmd;f)(e2)
{}\mRightarrow{} (bnum = (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e1))))
{}\mRightarrow{} (bnum = (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e2))))
{}\mRightarrow{} e1 \mleq{}loc e2
{}\mRightarrow{} (pvals1 = pvals2))
Date html generated:
2016_05_17-PM-03_43_28
Last ObjectModification:
2015_12_29-PM-11_17_54
Theory : paxos!synod
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