Step
*
of Lemma
pv11_p1_scout_fun_from_acc2
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀accpts,ldrs:bag(Id).
∀ldrs_uid:Id ─→ ℤ. ∀reps:bag(Id). ∀b:pv11_p1_Ballot_Num(). ∀p:pv11_p1_Ballot_Num() × ℤ × Cmd.
(pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ (p ∈ snd(pv11_p1_ScoutStateFun(Cmd;accpts;f;b;es;e)))
⇒ (↓∃e':E. ((e' < e) ∧ (p ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))))))
BY
{ (StartEmlProof
THEN (FLemma `pv11_p1_scout_fun_from_acc` [-1] THENA Auto)
THEN ExRepD
THEN (UseMessageConstraint (-2) THENA Auto)
THEN RepD
THEN D 0
THEN InstConcl [⌈e'@0⌉]⋅
THEN Auto) }
Latex:
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E.
\mforall{}accpts,ldrs:bag(Id). \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}reps:bag(Id). \mforall{}b:pv11\_p1\_Ballot\_Nu\000Cm().
\mforall{}p:pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd.
(pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} (p \mmember{} snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;f;b;es;e)))
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E. ((e' < e) \mwedge{} (p \mmember{} snd(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;e\000Cs;e'))))))
By
Latex:
(StartEmlProof
THEN (FLemma `pv11\_p1\_scout\_fun\_from\_acc` [-1] THENA Auto)
THEN ExRepD
THEN (UseMessageConstraint (-2) THENA Auto)
THEN RepD
THEN D 0
THEN InstConcl [\mkleeneopen{}e'@0\mkleeneclose{}]\mcdot{}
THEN Auto)
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