Nuprl Lemma : pv11_p1_valid-adopted-message_wf
∀Cmd:{T:Type| valueall-type(T)} . ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E.
(has-es-info-type(es;e;f;pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
⇒ (pv11_p1_valid-adopted-message(Cmd;es;e;f) ∈ ℙ))
Proof
Definitions occuring in Statement :
pv11_p1_valid-adopted-message: pv11_p1_valid-adopted-message(Cmd;es;e;f),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
has-es-info-type: has-es-info-type(es;e;f;T),
Message: Message(f),
event-ordering+: EO+(Info),
es-E: E,
list: T List,
valueall-type: valueall-type(T),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
product: x:A × B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
l_all: (∀x∈L.P[x]),
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
vatype: ValueAllType,
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
listp: A List+,
name: Name,
pv11_p1_headers: pv11_p1_headers(),
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
uimplies: b supposing a,
pv11_p1_headers_fun: pv11_p1_headers_fun(Cmd),
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,
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
nil: [],
it: ⋅,
null: null(as),
pv11_p1_valid-adopted-message: pv11_p1_valid-adopted-message(Cmd;es;e;f),
has-es-info-type: has-es-info-type(es;e;f;T),
pi2: snd(t)
Latex:
\mforall{}Cmd:\{T:Type| valueall-type(T)\} . \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E.
(has-es-info-type(es;e;f;pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List))
{}\mRightarrow{} (pv11\_p1\_valid-adopted-message(Cmd;es;e;f) \mmember{} \mBbbP{}))
Date html generated:
2016_05_17-PM-04_10_57
Last ObjectModification:
2015_12_29-PM-11_13_50
Theory : paxos!synod
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