Nuprl Lemma : pv11_p1_unique_adopted_fun
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀accpts,ldrs:bag(Id).
∀ldrs_uid:Id ─→ ℤ. ∀reps:bag(Id). ∀bnum:pv11_p1_Ballot_Num(). ∀pvals1,pvals2:(pv11_p1_Ballot_Num() × ℤ × Cmd) List.
(pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ <bnum, pvals1> ∈ pv11_p1_adopted'base(Cmd;f)(e1)
⇒ <bnum, pvals2> ∈ pv11_p1_adopted'base(Cmd;f)(e2)
⇒ (bnum = (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e1))) ∈ pv11_p1_Ballot_Num())
⇒ (bnum = (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e2))) ∈ pv11_p1_Ballot_Num())
⇒ e1 ≤loc e2
⇒ (pvals1 = pvals2 ∈ ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
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_LeaderStateFun: pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_adopted'base: pv11_p1_adopted'base(Cmd;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
pi1: fst(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T,
bag: bag(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-le_wf,
pv11_p1_LeaderStateFun_wf,
bool_wf,
list_wf,
classrel_wf,
pv11_p1_adopted'base_wf,
pv11_p1_message-constraint_wf,
pv11_p1_Ballot_Num_wf,
bag_wf,
Id_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,
pv11_p1_unique_adopted,
pv11_p1_LeaderState-classrel,
pair-eta,
subtype_rel_product,
top_wf,
subtype_top,
pi2_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e1,e2:E.
\mforall{}accpts,ldrs:bag(Id). \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}reps:bag(Id). \mforall{}bnum:pv11\_p1\_Ballot\000C\_Num().
\mforall{}pvals1,pvals2:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List.
(pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} <bnum, pvals1> \mmember{} pv11\_p1\_adopted'base(Cmd;f)(e1)
{}\mRightarrow{} <bnum, pvals2> \mmember{} pv11\_p1\_adopted'base(Cmd;f)(e2)
{}\mRightarrow{} (bnum = (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e1))))
{}\mRightarrow{} (bnum = (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e2))))
{}\mRightarrow{} e1 \mleq{}loc e2
{}\mRightarrow{} (pvals1 = pvals2))
Date html generated:
2015_07_23-PM-04_48_22
Last ObjectModification:
2015_02_04-AM-08_12_59
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