Nuprl Lemma : pv11_p1_scout_fun_from_acc2
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀accpts,ldrs:bag(Id).
∀ldrs_uid:Id ─→ ℤ. ∀reps:bag(Id). ∀b:pv11_p1_Ballot_Num(). ∀p:pv11_p1_Ballot_Num() × ℤ × Cmd.
(pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ (p ∈ snd(pv11_p1_ScoutStateFun(Cmd;accpts;f;b;es;e)))
⇒ (↓∃e':E. ((e' < e) ∧ (p ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;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_AcceptorStateFun: pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Message: Message(f),
event-ordering+: EO+(Info),
es-causl: (e < e'),
es-E: E,
Id: Id,
l_member: (x ∈ l),
vatype: ValueAllType,
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
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,
pv11_p1_scout_fun_from_acc,
base-noloc-classrel-make-Msg2,
hdrmkmsg_lemma,
msg-header_wf,
pv11_p1_headers_no_inputs_wf,
squash_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
es-causl_wf,
classrel_wf,
msg-interface_wf,
pv11_p1_main_wf,
make-msg-interface_wf,
es-loc_wf,
pv11_p1_ScoutStateFun_wf,
list_wf,
pv11_p1_message-constraint_wf,
pv11_p1_Ballot_Num_wf,
bag_wf,
Id_wf,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
pv11_p1_headers_type_wf,
set_wf,
valueall-type_wf,
msg-authentic_wf,
es-info_wf,
es-causl_transitivity2,
es-causle_weakening_locl,
and_wf,
pi2_wf,
pv11_p1_AcceptorStateFun_wf,
pv11_p1-p1b
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E.
\mforall{}accpts,ldrs:bag(Id). \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}reps:bag(Id). \mforall{}b:pv11\_p1\_Ballot\_Nu\000Cm().
\mforall{}p:pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd.
(pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} (p \mmember{} snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;f;b;es;e)))
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E. ((e' < e) \mwedge{} (p \mmember{} snd(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;e\000Cs;e'))))))
Date html generated:
2015_07_23-PM-04_46_22
Last ObjectModification:
2015_02_04-AM-08_25_31
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