Nuprl Lemma : pv11_p1-validity
∀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)
⇒ (∀e:E. ∀i:Id. ∀p:ℤ × Cmd.
(pv11_p1_decision'send(Cmd;f) i p ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e)
⇒ pv11_p1_valid-proposal(Cmd;es;e;p;f))))
Proof
Definitions occuring in Statement :
pv11_p1_valid-proposal: pv11_p1_valid-proposal(Cmd;es;e;p;f),
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,
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
bag: bag(T)
Lemmas :
pv11_p1_validity-lemma,
make-Msg-as-mk-msg,
bfalse_wf,
pv11_p1-decision,
sq_stable__es-causle,
event-ordering+_subtype,
Message_wf,
es-causle_weakening_locl,
base-classrel-equal,
subtype_rel_weakening,
ext-eq_weakening,
iff_weakening_equal,
es-causle_wf,
classrel_wf,
pv11_p1_propose'base_wf,
bag-member_wf,
squash_wf,
true_wf,
bag_wf,
pv11_p1_LeaderStateFun_wf,
bool_wf,
list_wf,
list-subtype-bag,
bag-member-sq-list-member,
pv11_p1_valid-proposal-transitivity,
l_all_iff,
l_member_wf,
pv11_p1_valid-proposal_wf,
es-info-body_wf,
map_wf,
member_map
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$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} (\mforall{}e:E. \mforall{}i:Id. \mforall{}p:\mBbbZ{} \mtimes{} Cmd.
(pv11\_p1\_decision'send(Cmd;f) i p \mmember{} pv11\_p1\_main(Cmd;accpts;ldrs;ldrs$_{uid}\000C$;reps;f)(e)
{}\mRightarrow{} pv11\_p1\_valid-proposal(Cmd;es;e;p;f))))
Date html generated:
2015_07_23-PM-05_06_16
Last ObjectModification:
2015_02_04-AM-07_49_56
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