Nuprl Lemma : pv11_p1-validity2
∀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)
⇒ for every p1 in pv11_p1_decision'base(Cmd;f) there is an
earlier event with info=m such that
(msg-header(m) = [propose] ∈ Name) ∧ (p1 = msg-body(m) ∈ (ℤ × 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),
msg-body: msg-body(msg),
msg-header: msg-header(m),
Message: Message(f),
causal-class-relation: causal-class-relation,
event-ordering+: EO+(Info),
Id: Id,
name: Name,
cons: [a / b],
nil: [],
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
token: "$token",
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
pv11_p1-validity,
classrel_wf,
Message_wf,
pv11_p1_decision'base_wf,
es-E_wf,
event-ordering+_subtype,
base-noloc-classrel-make-Msg2,
cons_wf_listp,
nil_wf,
listp_wf,
hdrmkmsg_lemma,
cons_member,
cons_wf,
name_wf,
l_member_wf,
equal-wf-base,
msg-header_wf,
pv11_p1_headers_no_inputs_wf,
squash_wf,
exists_wf,
es-causl_wf,
msg-interface_wf,
pv11_p1_main_wf,
make-msg-interface_wf,
es-loc_wf,
mk-msg_wf,
msg-authentic_wf,
es-info_wf,
subtype_rel_weakening,
ext-eq_weakening,
pv11_p1-decision,
subtype_base_sq,
bool_wf,
bool_subtype_base,
make-Msg-as-mk-msg,
base-noloc-classrel,
es-causl_transitivity1,
equal-wf-T-base,
msg-body_wf2,
subtype_rel-equal,
msg-type_wf,
iff_weakening_equal
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}accpts,ldrs:bag(Id).
\mforall{}ldrs$_{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{} for every p1 in pv11\_p1\_decision'base(Cmd;f) there is an
earlier event with info=m such that
(msg-header(m) = [propose]) \mwedge{} (p1 = msg-body(m)))
Date html generated:
2015_07_23-PM-05_06_23
Last ObjectModification:
2015_02_04-AM-07_49_38
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