Nuprl Lemma : pv11_p1_scout_fun_from_acc
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀accpts:bag(Id).
∀b:pv11_p1_Ballot_Num(). ∀p:pv11_p1_Ballot_Num() × ℤ × Cmd.
((p ∈ snd(pv11_p1_ScoutStateFun(Cmd;accpts;f;b;es;e)))
⇒ (∃e':E
∃l:Id
∃r:(pv11_p1_Ballot_Num() × ℤ × Cmd) List. (e' ≤loc e ∧ <l, b, b, r> ∈ pv11_p1_p1b'base(Cmd;f)(e') ∧ (p ∈ r))))
Proof
Definitions occuring in Statement :
pv11_p1_ScoutStateFun: pv11_p1_ScoutStateFun(Cmd;accpts;mf;x;es;e),
pv11_p1_p1b'base: pv11_p1_p1b'base(Cmd;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
Id: Id,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
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_scout_from_acc,
pv11_p1_ScoutStateFun_wf,
pv11_p1_ScoutState-classrel,
bag_wf,
Id_wf,
list_wf,
all_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
es-le_wf,
classrel_wf,
pv11_p1_p1b'base_wf,
pv11_p1_Ballot_Num_wf,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
pv11_p1_headers_type_wf,
set_wf,
valueall-type_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}accpts:bag(Id).
\mforall{}b:pv11\_p1\_Ballot\_Num(). \mforall{}p:pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd.
((p \mmember{} snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;f;b;es;e)))
{}\mRightarrow{} (\mexists{}e':E
\mexists{}l:Id
\mexists{}r:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List
(e' \mleq{}loc e \mwedge{} <l, b, b, r> \mmember{} pv11\_p1\_p1b'base(Cmd;f)(e') \mwedge{} (p \mmember{} r))))
Date html generated:
2015_07_23-PM-04_46_18
Last ObjectModification:
2015_02_04-AM-08_25_23
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