Nuprl Lemma : pv11_p1_pmax_desc_iff
∀Cmd:ValueAllType. ∀ldrs_uid:Id ⟶ ℤ. ∀pvals:(pv11_p1_Ballot_Num() × ℤ × Cmd) List. ∀s:ℤ. ∀c:Cmd.
((<s, c> ∈ pv11_p1_pmax(Cmd;ldrs_uid) pvals)
⇐⇒ ∃b:pv11_p1_Ballot_Num()
((<b, s, c> ∈ pvals)
∧ (∀b':pv11_p1_Ballot_Num(). ∀c':Cmd. ((<b', s, c'> ∈ pvals) ⇒ (↑(pv11_p1_leq_bnum(ldrs_uid) b' b))))))
Proof
Definitions occuring in Statement :
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
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],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
let: let,
so_lambda: λ2x.t[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff,
so_apply: x[s],
cand: A c∧ B,
pi2: snd(t),
not: ¬A,
sq_type: SQType(T),
guard: {T},
false: False
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}pvals:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd\000C) List. \mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
((<s, c> \mmember{} pv11\_p1\_pmax(Cmd;ldrs$_{uid}$) pvals)
\mLeftarrow{}{}\mRightarrow{} \mexists{}b:pv11\_p1\_Ballot\_Num()
((<b, s, c> \mmember{} pvals)
\mwedge{} (\mforall{}b':pv11\_p1\_Ballot\_Num(). \mforall{}c':Cmd.
((<b', s, c'> \mmember{} pvals) {}\mRightarrow{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b' b))))\000C))
Date html generated:
2016_05_17-PM-03_16_46
Last ObjectModification:
2015_12_29-PM-11_20_46
Theory : paxos!synod
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