Nuprl Lemma : pv11_p1_A3
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀ldrs_uid:Id ⟶ ℤ.
∀bnum1,bnum2:pv11_p1_Ballot_Num(). ∀accepted1,accepted2:(pv11_p1_Ballot_Num() × ℤ × Cmd) List.
((e1 <loc e2)
⇒ <bnum1, accepted1> ∈ pv11_p1_AcceptorState(Cmd;ldrs_uid;f)(e1)
⇒ <bnum2, accepted2> ∈ pv11_p1_AcceptorState(Cmd;ldrs_uid;f)(e2)
⇒ (∀pv:pv11_p1_Ballot_Num() × ℤ × Cmd. ((pv ∈ accepted1) ⇒ (pv ∈ accepted2))))
Proof
Definitions occuring in Statement :
pv11_p1_AcceptorState: pv11_p1_AcceptorState(Cmd;ldrs_uid;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-locl: (e <loc e'),
es-E: E,
Id: Id,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ
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)
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e1,e2:E.
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}bnum1,bnum2:pv11\_p1\_Ballot\_Num(). \mforall{}accepted1,accepted2:(\000Cpv11\_p1\_Ballot\_Num()
\mtimes{} \mBbbZ{}
\mtimes{} Cmd) List.
((e1 <loc e2)
{}\mRightarrow{} <bnum1, accepted1> \mmember{} pv11\_p1\_AcceptorState(Cmd;ldrs$_{uid}$;f)(e1)
{}\mRightarrow{} <bnum2, accepted2> \mmember{} pv11\_p1\_AcceptorState(Cmd;ldrs$_{uid}$;f)(e2)
{}\mRightarrow{} (\mforall{}pv:pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd. ((pv \mmember{} accepted1) {}\mRightarrow{} (pv \mmember{} accepted2))))
Date html generated:
2016_05_17-PM-03_59_12
Last ObjectModification:
2015_12_29-PM-11_15_40
Theory : paxos!synod
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