Nuprl Lemma : pv11_p1_messages-delivered-w-omissions-accpts_wf
∀[Cmd:{T:Type| valueall-type(T)} ]. ∀[f:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(f))]. ∀[accpts,ldrs:bag(Id)].
∀[ldrs_uid:Id ⟶ ℤ]. ∀[reps:bag(Id)]. ∀[flrs:ℤ].
(pv11_p1_messages-delivered-w-omissions-accpts{i:l}(es;flrs;Cmd;accpts;ldrs;ldrs_uid;reps;f) ∈ ℙ')
Proof
Definitions occuring in Statement :
pv11_p1_messages-delivered-w-omissions-accpts: pv11_p1_messages-delivered-w-omissions-accpts{i:l}(es;flrs;Cmd;accpts;ldrs;ldrs_uid;reps;f),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
Message: Message(f),
event-ordering+: EO+(Info),
Id: Id,
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
subtype_rel: A ⊆r B,
listp: A List+,
name: Name,
vatype: ValueAllType,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
sq_stable: SqStable(P),
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
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),
squash: ↓T,
pv11_p1_messages-delivered-w-omissions-accpts: pv11_p1_messages-delivered-w-omissions-accpts{i:l}(es;flrs;Cmd;accpts;ldrs;ldrs_uid;reps;f)
Latex:
\mforall{}[Cmd:\{T:Type| valueall-type(T)\} ]. \mforall{}[f:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(f))].
\mforall{}[accpts,ldrs:bag(Id)]. \mforall{}[ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}]. \mforall{}[reps:bag(Id)]. \mforall{}[flrs:\mBbbZ{}].
(pv11\_p1\_messages-delivered-w-omissions-accpts\{i:l\}(es;flrs;Cmd;accpts;ldrs;ldrs$_{uid\000C}$;reps;f) \mmember{} \mBbbP{}')
Date html generated:
2016_05_17-PM-04_18_12
Last ObjectModification:
2016_01_08-PM-05_39_10
Theory : paxos!synod
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