Nuprl Lemma : pv11_p1_scout_state_subset_pvals
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀bnum:pv11_p1_Ballot_Num().
∀accpts,ldrs:bag(Id). ∀ldrs_uid:Id ─→ ℤ. ∀reps:bag(Id).
(Inj(Id;ℤ;ldrs_uid)
⇒ pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ (header(e) = ``pv11_p1 p1b`` ∈ Name)
⇒ has-es-info-type(es;e;f;Id × pv11_p1_Ballot_Num() × pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
⇒ ((fst(snd(msgval(e)))) = bnum ∈ pv11_p1_Ballot_Num())
⇒ ((fst(snd(snd(msgval(e))))) = bnum ∈ pv11_p1_Ballot_Num())
⇒ (↓l_subset(pv11_p1_Ballot_Num()
× ℤ
× Cmd;snd(snd(snd(msgval(e))));snd(pv11_p1_ScoutStateFun(Cmd;accpts;f;bnum;es;e)))))
Proof
Definitions occuring in Statement :
pv11_p1_message-constraint: pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; mf; es),
pv11_p1_ScoutStateFun: pv11_p1_ScoutStateFun(Cmd;accpts;mf;x;es;e),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
es-info-body: msgval(e),
has-es-info-type: has-es-info-type(es;e;f;T),
es-header: header(e),
Message: Message(f),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
name: Name,
l_subset: l_subset(T;as;bs),
cons: [a / b],
nil: [],
list: T List,
inject: Inj(A;B;f),
vatype: ValueAllType,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
token: "$token",
equal: s = t ∈ T,
bag: bag(T)
Definitions :
assert: ↑b,
ifthenelse: if b then t else f fi ,
deq-member: x ∈b L),
reduce: reduce(f;k;as),
pv11_p1_headers_no_inputs: pv11_p1_headers_no_inputs(),
cons: [a / b],
bor: p ∨bq,
list-deq: list-deq(eq),
band: p ∧b q,
atom-deq: AtomDeq,
eq_atom: x =a y,
btrue: tt,
bfalse: ff,
nil: [],
it: ⋅,
null: null(as),
true: True,
member: t ∈ T
Lemmas :
int_seg_wf,
length_wf,
name_wf,
pv11_p1_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
pv11_p1_headers_fun_wf,
cons_wf_listp,
nil_wf,
listp_wf,
cons_member,
cons_wf,
equal-wf-base,
iff_weakening_equal,
es-info-body_wf,
has-es-info-type_wf,
list_wf,
equal-wf-T-base,
es-header_wf,
pv11_p1_message-constraint_wf,
inject_wf,
bag_wf,
Id_wf,
pv11_p1_Ballot_Num_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
pv11_p1_headers_type_wf,
set_wf,
valueall-type_wf,
member-eclass_wf,
pv11_p1_p1b'base_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
squash_wf,
true_wf,
l_subset_wf,
pi2_wf,
pv11_p1_scout_state_fun_eq,
classfun-res-base,
pv11_p1_eq_bnums_wf,
pv11_p1_eq_bnums-assert,
and_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
subtype_top,
list_subtype_base,
atom_subtype_base,
assert-deq-member,
pv11_p1_headers_no_inputs_wf,
es-info-mk-msg,
event-ordering+_cumulative,
es-info-auth_wf,
subtype_rel_weakening,
ext-eq_weakening,
classrel_wf,
msg-interface_wf,
pv11_p1_main_wf,
make-msg-interface_wf,
es-loc_wf,
pair-eta,
mk-msg_wf,
pv11_p1-p1b,
pv11_p1_append_news_iff,
append_wf,
exists_wf,
pv11_p1_AcceptorStateFun_wf,
member_append,
nil_member,
pv11_p1_ScoutStateFun_wf,
es-pred_wf,
pv11_p1_append_news_iff2,
pv11_p1_scout_fun_from_acc2,
assert-member-eclass,
base-classrel-equal
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E.
\mforall{}bnum:pv11\_p1\_Ballot\_Num(). \mforall{}accpts,ldrs:bag(Id). \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}reps:b\000Cag(Id).
(Inj(Id;\mBbbZ{};ldrs$_{uid}$)
{}\mRightarrow{} pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid\mbackslash{}ff7\000Cd$; reps; f; es)
{}\mRightarrow{} (header(e) = ``pv11\_p1 p1b``)
{}\mRightarrow{} has-es-info-type(es;e;f;Id
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List))
{}\mRightarrow{} ((fst(snd(msgval(e)))) = bnum)
{}\mRightarrow{} ((fst(snd(snd(msgval(e))))) = bnum)
{}\mRightarrow{} (\mdownarrow{}l\_subset(pv11\_p1\_Ballot\_Num()
\mtimes{} \mBbbZ{}
\mtimes{} Cmd;snd(snd(snd(msgval(e))));snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;f;bnum;es;e)))))
Date html generated:
2015_07_23-PM-04_54_40
Last ObjectModification:
2015_02_04-AM-07_58_10
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