Nuprl Lemma : pv11_p1_A4_C1_funA
∀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). ∀b:pv11_p1_Ballot_Num(). ∀s:ℤ. ∀p1,p2:Cmd.
(Inj(Id;ℤ;ldrs_uid)
⇒ pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ (<b, s, p1> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e1)))
⇒ (<b, s, p2> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e2)))
⇒ (p1 = p2 ∈ Cmd))
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_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-E: E,
Id: Id,
l_member: (x ∈ l),
inject: Inj(A;B;f),
vatype: ValueAllType,
pi2: snd(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,
pv11_p1_AcceptorStateFun_wf,
list_wf,
pv11_p1_message-constraint_wf,
inject_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,
es-loc_wf,
pair-eta,
subtype_rel_product,
top_wf,
subtype_top,
pv11_p1_AcceptorState-classrel,
classrel_wf,
msg-interface_wf,
pv11_p1_main_wf,
pv11_p1_p2a'send_wf,
pv11_p1_A4_C1
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{}b:pv11\_p1\_Ballot\_Nu\000Cm(). \mforall{}s:\mBbbZ{}. \mforall{}p1,p2:Cmd.
(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{} (<b, s, p1> \mmember{} snd(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;es;e1)))
{}\mRightarrow{} (<b, s, p2> \mmember{} snd(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;es;e2)))
{}\mRightarrow{} (p1 = p2))
Date html generated:
2015_07_23-PM-04_54_06
Last ObjectModification:
2015_02_04-AM-07_57_21
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