Nuprl Lemma : pv11_p1_leader_propose_wf
∀[Cmd:ValueAllType]
  (pv11_p1_leader_propose(Cmd) ∈ Id
   ⟶ (ℤ × Cmd)
   ⟶ (pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List))
   ⟶ bag(pv11_p1_Ballot_Num() × ℤ × Cmd))
Proof
Definitions occuring in Statement : 
pv11_p1_leader_propose: pv11_p1_leader_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
, 
bag: bag(T)
Definitions unfolded in proof : 
vatype: ValueAllType
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
pv11_p1_leader_propose: pv11_p1_leader_propose(Cmd)
, 
spreadn: spread3, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
band: p ∧b q
, 
ifthenelse: if b then t else f fi 
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
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
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
Latex:
\mforall{}[Cmd:ValueAllType]
    (pv11\_p1\_leader\_propose(Cmd)  \mmember{}  Id
      {}\mrightarrow{}  (\mBbbZ{}  \mtimes{}  Cmd)
      {}\mrightarrow{}  (pv11\_p1\_Ballot\_Num()  \mtimes{}  \mBbbB{}  \mtimes{}  ((\mBbbZ{}  \mtimes{}  Cmd)  List))
      {}\mrightarrow{}  bag(pv11\_p1\_Ballot\_Num()  \mtimes{}  \mBbbZ{}  \mtimes{}  Cmd))
Date html generated:
2016_05_17-PM-02_57_11
Last ObjectModification:
2015_12_29-PM-11_23_56
Theory : paxos!synod
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