Nuprl Lemma : pv11_p1-validity
∀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)
⇒ (∀e:E. ∀i:Id. ∀p:ℤ × Cmd.
(pv11_p1_decision'send(Cmd;f) i p ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e)
⇒ pv11_p1_valid-proposal(Cmd;es;e;p;f))))
Proof
Definitions occuring in Statement :
pv11_p1_valid-proposal: pv11_p1_valid-proposal(Cmd;es;e;p;f),
pv11_p1_decision'send: pv11_p1_decision'send(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_main: pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
msg-interface: Interface,
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ,
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),
pv11_p1_valid-proposal: pv11_p1_valid-proposal(Cmd;es;e;p;f),
pv11_p1_decision'send: pv11_p1_decision'send(Cmd;f),
top: Top,
mk-msg-interface: mk-msg-interface(l;m),
make-msg-interface: make-msg-interface(i;l;m),
exists: ∃x:A. B[x],
or: P ∨ Q,
cand: A c∧ B,
has-es-info-type: has-es-info-type(es;e;f;T),
sq_stable: SqStable(P),
pv11_p1_propose'base: pv11_p1_propose'base(Cmd;mf),
encodes-msg-type: hdr encodes T,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
equal-info-body: v = body(e),
pv11_p1_valid-LeaderState: pv11_p1_valid-LeaderState(Cmd;ldrs_uid;es;e;f),
pv11_p1_valid-proposals: pv11_p1_valid-proposals(Cmd;es;e;L;f),
pi2: snd(t),
pi1: fst(t),
pv11_p1_valid-adopted-message: pv11_p1_valid-adopted-message(Cmd;es;e;f)
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$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} (\mforall{}e:E. \mforall{}i:Id. \mforall{}p:\mBbbZ{} \mtimes{} Cmd.
(pv11\_p1\_decision'send(Cmd;f) i p \mmember{} pv11\_p1\_main(Cmd;accpts;ldrs;ldrs$_{uid}\000C$;reps;f)(e)
{}\mRightarrow{} pv11\_p1\_valid-proposal(Cmd;es;e;p;f))))
Date html generated:
2016_05_17-PM-04_18_46
Last ObjectModification:
2016_01_18-AM-11_15_46
Theory : paxos!synod
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