Nuprl Lemma : pv11_p1-agreement2
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀accpts,ldrs:bag(Id). ∀ldrs_uid:Id ─→ ℤ.
∀reps:bag(Id).
(pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ Inj(Id;ℤ;ldrs_uid)
⇒ any p1,p2 from pv11_p1_decision'base(Cmd;f) satisfy
((fst(p1)) = (fst(p2)) ∈ ℤ) ⇒ ((snd(p1)) = (snd(p2)) ∈ Cmd))
Proof
Definitions occuring in Statement :
pv11_p1_decision'base: pv11_p1_decision'base(Cmd;f),
pv11_p1_message-constraint: pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; mf; es),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
Message: Message(f),
consistent-class: consistent-class,
event-ordering+: EO+(Info),
Id: Id,
inject: Inj(A;B;f),
vatype: ValueAllType,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
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,
pv11_p1_Ballot_Num_wf,
list_wf,
classrel_wf,
pv11_p1_decision'base_wf,
es-E_wf,
event-ordering+_subtype,
inject_wf,
pv11_p1_message-constraint_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,
base-noloc-classrel-make-Msg2,
hdrmkmsg_lemma,
msg-header_wf,
pv11_p1_headers_no_inputs_wf,
squash_wf,
exists_wf,
es-causl_wf,
msg-interface_wf,
pv11_p1_main_wf,
make-msg-interface_wf,
es-loc_wf,
msg-authentic_wf,
es-info_wf,
subtype_base_sq,
int_subtype_base,
pv11_p1-decision,
bool_wf,
bool_subtype_base,
pv11_p1-agreement
Latex:
\mforall{}Cmd:ValueAllType. \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).
(pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} Inj(Id;\mBbbZ{};ldrs$_{uid}$)
{}\mRightarrow{} any p1,p2 from pv11\_p1\_decision'base(Cmd;f) satisfy
((fst(p1)) = (fst(p2))) {}\mRightarrow{} ((snd(p1)) = (snd(p2))))
Date html generated:
2015_07_23-PM-05_06_36
Last ObjectModification:
2015_02_04-AM-07_49_48
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