Nuprl Lemma : pv11_p1_scout_fun_from_acc
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀accpts:bag(Id).
∀b:pv11_p1_Ballot_Num(). ∀p:pv11_p1_Ballot_Num() × ℤ × Cmd.
((p ∈ snd(pv11_p1_ScoutStateFun(Cmd;accpts;f;b;es;e)))
⇒ (∃e':E
∃l:Id
∃r:(pv11_p1_Ballot_Num() × ℤ × Cmd) List. (e' ≤loc e ∧ <l, b, b, r> ∈ pv11_p1_p1b'base(Cmd;f)(e') ∧ (p ∈ r))))
Proof
Definitions occuring in Statement :
pv11_p1_ScoutStateFun: pv11_p1_ScoutStateFun(Cmd;accpts;mf;x;es;e),
pv11_p1_p1b'base: pv11_p1_p1b'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,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
pair: <a, b>,
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,
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),
pi2: snd(t),
exists: ∃x:A. B[x]
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}accpts:bag(Id).
\mforall{}b:pv11\_p1\_Ballot\_Num(). \mforall{}p:pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd.
((p \mmember{} snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;f;b;es;e)))
{}\mRightarrow{} (\mexists{}e':E
\mexists{}l:Id
\mexists{}r:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List
(e' \mleq{}loc e \mwedge{} <l, b, b, r> \mmember{} pv11\_p1\_p1b'base(Cmd;f)(e') \mwedge{} (p \mmember{} r))))
Date html generated:
2016_05_17-PM-03_19_46
Last ObjectModification:
2015_12_29-PM-11_18_55
Theory : paxos!synod
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