Nuprl Lemma : pv11_p1-agreement
∀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). ∀i1,i2:Id. ∀s:ℤ. ∀c1,c2:Cmd.
(pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ Inj(Id;ℤ;ldrs_uid)
⇒ pv11_p1_decision'send(Cmd;f) i1 <s, c1> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e1)
⇒ pv11_p1_decision'send(Cmd;f) i2 <s, c2> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e2)
⇒ (c1 = c2 ∈ Cmd))
Proof
Definitions occuring in Statement :
pv11_p1_decision'send: pv11_p1_decision'send(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_main: pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
msg-interface: Interface,
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
inject: Inj(A;B;f),
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
int: ℤ,
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,
pv11_p1_Ballot_Num_wf,
list_wf,
classrel_wf,
msg-interface_wf,
pv11_p1_main_wf,
pv11_p1_decision'send_wf,
inject_wf,
pv11_p1_message-constraint_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,
make-Msg-as-mk-msg,
bfalse_wf,
subtype_base_sq,
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,
es-info-body_wf,
subtype_rel_transitivity,
es-info-type_wf,
subtype_rel_weakening,
ext-eq_weakening,
make-msg-interface_wf,
es-loc_wf,
pair-eta,
subtype_rel_product,
top_wf,
subtype_top,
mk-msg_wf,
pi1_wf_top,
bag-member_wf,
pv11_p1-decision,
pv11_p1-p2b,
sq_stable__has-es-info-type,
pv11_p1_leq_bnum_or,
make-Msg_wf,
exists_wf,
pv11_p1_decision_from_p2a_acc,
base-classrel-equal,
and_wf,
pi2_wf,
equal-wf-T-base,
es-header_wf,
subtype_rel-equal,
es-le_wf,
pv11_p1_ScoutStateFun_wf,
eo-forward_wf,
member-eo-forward-E,
pv11_p1_AcceptorStateFun_wf,
pv11_p1_consistency_lemma
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{}i1,i2:Id. \mforall{}s:\mBbbZ{}. \mforall{}c1\000C,c2:Cmd.
(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}$)
{}\mRightarrow{} pv11\_p1\_decision'send(Cmd;f) i1 <s, c1> \mmember{} pv11\_p1\_main(Cmd;accpts;ldrs;ldrs$_{uid\mbackslash{}f\000Cf7d$;reps;f)(e1)
{}\mRightarrow{} pv11\_p1\_decision'send(Cmd;f) i2 <s, c2> \mmember{} pv11\_p1\_main(Cmd;accpts;ldrs;ldrs$_{uid\mbackslash{}f\000Cf7d$;reps;f)(e2)
{}\mRightarrow{} (c1 = c2))
Date html generated:
2015_07_23-PM-05_06_30
Last ObjectModification:
2015_02_04-AM-07_51_47
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