Nuprl Lemma : pv11_p1_headers-property
∀[Cmd:ValueAllType]
∀f:pv11_p1_headers_type{i:l}(Cmd)
(((f ``pv11_p1 p1a``) = (Id × pv11_p1_Ballot_Num()) ∈ Type)
∧ ((f ``pv11_p1 p1b``)
= (Id × pv11_p1_Ballot_Num() × pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
∈ Type)
∧ ((f ``pv11_p1 p2a``) = (Id × pv11_p1_Ballot_Num() × ℤ × Cmd) ∈ Type)
∧ ((f ``pv11_p1 p2b``) = (Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()) ∈ Type)
∧ ((f ``pv11_p1 preempted``) = pv11_p1_Ballot_Num() ∈ Type)
∧ ((f ``pv11_p1 adopted``) = (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)) ∈ Type)
∧ ((f [propose]) = (ℤ × Cmd) ∈ Type)
∧ ((f [decision]) = (ℤ × Cmd) ∈ Type))
Proof
Definitions occuring in Statement :
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
cons: [a / b],
nil: [],
list: T List,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
apply: f a,
product: x:A × B[x],
int: ℤ,
token: "$token",
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
vatype: ValueAllType,
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
listp: A List+,
name: Name,
pv11_p1_headers: pv11_p1_headers(),
rev_implies: P ⇐ Q,
or: P ∨ Q,
uimplies: b supposing a,
guard: {T},
pv11_p1_headers_fun: pv11_p1_headers_fun(Cmd),
ifthenelse: if b then t else f fi ,
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
list_ind: list_ind,
cons: [a / b],
band: p ∧b q,
atom-deq: AtomDeq,
eq_atom: x =a y,
btrue: tt,
nil: [],
it: ⋅,
null: null(as),
bfalse: ff
Latex:
\mforall{}[Cmd:ValueAllType]
\mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd)
(((f ``pv11\_p1 p1a``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num()))
\mwedge{} ((f ``pv11\_p1 p1b``)
= (Id
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
\mwedge{} ((f ``pv11\_p1 p2a``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd))
\mwedge{} ((f ``pv11\_p1 p2b``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num()))
\mwedge{} ((f ``pv11\_p1 preempted``) = pv11\_p1\_Ballot\_Num())
\mwedge{} ((f ``pv11\_p1 adopted``) = (pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
\mwedge{} ((f [propose]) = (\mBbbZ{} \mtimes{} Cmd))
\mwedge{} ((f [decision]) = (\mBbbZ{} \mtimes{} Cmd)))
Date html generated:
2016_05_17-PM-03_12_31
Last ObjectModification:
2015_12_29-PM-11_22_50
Theory : paxos!synod
Home
Index