Nuprl Lemma : pv11_p1_CommanderState-classrel
∀[Cmd:ValueAllType]. ∀[accpts:bag(Id)]. ∀[mf:pv11_p1_headers_type{i:l}(Cmd)].
∀es:EO+(Message(mf)). ∀e:E. ∀x:pv11_p1_Ballot_Num(). ∀zzs:ℤ. ∀v:bag(Id).
(v ∈ pv11_p1_CommanderState(Cmd;accpts;mf) x zzs(e)
⇐⇒ v = pv11_p1_CommanderStateFun(Cmd;accpts;mf;x;zzs;es;e) ∈ bag(Id))
Proof
Definitions occuring in Statement :
pv11_p1_CommanderStateFun: pv11_p1_CommanderStateFun(Cmd;accpts;mf;x;zzs;es;e),
pv11_p1_CommanderState: pv11_p1_CommanderState(Cmd;accpts;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-E: E,
Id: Id,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
apply: f a,
int: ℤ,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
subtype_rel: A ⊆r B,
listp: A List+,
name: Name,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
sq_stable: SqStable(P),
l_all: (∀x∈L.P[x]),
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
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),
uiff: uiff(P;Q),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
pv11_p1_CommanderStateFun: pv11_p1_CommanderStateFun(Cmd;accpts;mf;x;zzs;es;e),
rev_uimplies: rev_uimplies(P;Q),
classrel: v ∈ X(e),
bag-member: x ↓∈ bs
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[accpts:bag(Id)]. \mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)].
\mforall{}es:EO+(Message(mf)). \mforall{}e:E. \mforall{}x:pv11\_p1\_Ballot\_Num(). \mforall{}zzs:\mBbbZ{}. \mforall{}v:bag(Id).
(v \mmember{} pv11\_p1\_CommanderState(Cmd;accpts;mf) x zzs(e)
\mLeftarrow{}{}\mRightarrow{} v = pv11\_p1\_CommanderStateFun(Cmd;accpts;mf;x;zzs;es;e))
Date html generated:
2016_05_17-PM-02_53_32
Last ObjectModification:
2016_01_18-AM-11_22_26
Theory : paxos!synod
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