Nuprl Lemma : pv11_p1-agreement2
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀accpts,ldrs:bag(Id). ∀ldrs_uid:Id ⟶ ℤ.
∀reps:bag(Id).
(pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ Inj(Id;ℤ;ldrs_uid)
⇒ any p1,p2 from pv11_p1_decision'base(Cmd;f) satisfy
((fst(p1)) = (fst(p2)) ∈ ℤ) ⇒ ((snd(p1)) = (snd(p2)) ∈ Cmd))
Proof
Definitions occuring in Statement :
pv11_p1_decision'base: pv11_p1_decision'base(Cmd;f),
pv11_p1_message-constraint: pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; mf; es),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
Message: Message(f),
consistent-class: consistent-class,
event-ordering+: EO+(Info),
Id: Id,
inject: Inj(A;B;f),
vatype: ValueAllType,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
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),
consistent-class: consistent-class,
pi1: fst(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),
pv11_p1_decision'base: pv11_p1_decision'base(Cmd;f),
uiff: uiff(P;Q),
es-header: header(e),
pv11_p1_headers_no_inputs: pv11_p1_headers_no_inputs(),
top: Top,
squash: ↓T,
exists: ∃x:A. B[x],
make-msg-interface: make-msg-interface(i;l;m),
sq_type: SQType(T),
pv11_p1_init_active: pv11_p1_init_active(),
pv11_p1_decision'send: pv11_p1_decision'send(Cmd;f),
mk-msg: mk-msg(auth;hdr;val),
make-Msg: make-Msg(hdr;val),
mk-msg-interface: mk-msg-interface(l;m)
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}accpts,ldrs:bag(Id).
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}reps:bag(Id).
(pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} Inj(Id;\mBbbZ{};ldrs$_{uid}$)
{}\mRightarrow{} any p1,p2 from pv11\_p1\_decision'base(Cmd;f) satisfy
((fst(p1)) = (fst(p2))) {}\mRightarrow{} ((snd(p1)) = (snd(p2))))
Date html generated:
2016_05_17-PM-04_19_36
Last ObjectModification:
2015_12_29-PM-11_15_12
Theory : paxos!synod
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