Nuprl Lemma : pv11_p1_on_propose_wf
∀[Cmd:ValueAllType]
(pv11_p1_on_propose(Cmd) ∈ Id
⟶ (ℤ × Cmd)
⟶ (pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List))
⟶ (pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List)))
Proof
Definitions occuring in Statement :
pv11_p1_on_propose: pv11_p1_on_propose(Cmd),
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_on_propose: pv11_p1_on_propose(Cmd),
spreadn: spread3,
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 ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B
Latex:
\mforall{}[Cmd:ValueAllType]
(pv11\_p1\_on\_propose(Cmd) \mmember{} Id
{}\mrightarrow{} (\mBbbZ{} \mtimes{} Cmd)
{}\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_09
Last ObjectModification:
2015_12_29-PM-11_24_24
Theory : paxos!synod
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