Nuprl Lemma : pv11_p1_when_adopted_wf
∀[Cmd:ValueAllType]. ∀[ldrs_uid:Id ⟶ ℤ].
(pv11_p1_when_adopted(Cmd;ldrs_uid) ∈ Id
⟶ (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
⟶ (pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List))
⟶ (pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List)))
Proof
Definitions occuring in Statement :
pv11_p1_when_adopted: pv11_p1_when_adopted(Cmd;ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
list: T List,
vatype: ValueAllType,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
pv11_p1_when_adopted: pv11_p1_when_adopted(Cmd;ldrs_uid),
spreadn: spread3,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}].
(pv11\_p1\_when\_adopted(Cmd;ldrs$_{uid}$) \mmember{} Id
{}\mrightarrow{} (pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List))
{}\mrightarrow{} (pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbB{} \mtimes{} ((\mBbbZ{} \mtimes{} Cmd) List))
{}\mrightarrow{} (pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbB{} \mtimes{} ((\mBbbZ{} \mtimes{} Cmd) List)))
Date html generated:
2016_05_17-PM-02_56_16
Last ObjectModification:
2015_12_29-PM-11_24_30
Theory : paxos!synod
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