Nuprl Lemma : pv11_p1_on_p2a_wf
∀[Cmd:ValueAllType]. ∀[ldrs_uid:Id ⟶ ℤ].
(pv11_p1_on_p2a(Cmd;ldrs_uid) ∈ Id
⟶ (Id × pv11_p1_Ballot_Num() × ℤ × Cmd)
⟶ (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
⟶ (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
Proof
Definitions occuring in Statement :
pv11_p1_on_p2a: pv11_p1_on_p2a(Cmd;ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
list: T List,
vatype: ValueAllType,
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_on_p2a: pv11_p1_on_p2a(Cmd;ldrs_uid),
so_lambda: λ2x.t[x],
so_apply: x[s],
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,
subtype_rel: A ⊆r B,
bfalse: ff
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}].
(pv11\_p1\_on\_p2a(Cmd;ldrs$_{uid}$) \mmember{} Id
{}\mrightarrow{} (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd)
{}\mrightarrow{} (pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List))
{}\mrightarrow{} (pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
Date html generated:
2016_05_17-PM-02_51_29
Last ObjectModification:
2015_12_29-PM-11_26_59
Theory : paxos!synod
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