Nuprl Lemma : pv11_p1_ldr_fun_proposal3
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀ldrs_uid:Id ─→ ℤ. ∀s:ℤ. ∀c:Cmd.
((<s, c> ∈ snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e))))
⇒ (∃e':E
((e' <loc e)
∧ (∀e'':E. ((e' <loc e'') ⇒ e'' ≤loc e ⇒ (<s, c> ∈ snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e''))))))
∧ ((<s, c> ∈ pv11_p1_propose'base(Cmd;f)(e')
∧ (¬↑(pv11_p1_in_domain(Cmd) s (snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e')))))))
∨ (∃pvals:(pv11_p1_Ballot_Num() × ℤ × Cmd) List
∃b:pv11_p1_Ballot_Num()
(<fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e')), pvals> ∈ pv11_p1_adopted'base(Cmd;f)(e')
∧ (<b, s, c> ∈ pvals)
∧ (∀b':pv11_p1_Ballot_Num(). ∀c':Cmd.
((<b', s, c'> ∈ pvals) ⇒ (↑(pv11_p1_leq_bnum(ldrs_uid) b' b))))))))))
Proof
Definitions occuring in Statement :
pv11_p1_LeaderStateFun: pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_propose'base: pv11_p1_propose'base(Cmd;mf),
pv11_p1_adopted'base: pv11_p1_adopted'base(Cmd;mf),
pv11_p1_in_domain: pv11_p1_in_domain(Cmd),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
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-locl: (e <loc e'),
es-E: E,
Id: Id,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
assert: ↑b,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ
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,
list_wf,
pv11_p1_ldr_proposal3,
pv11_p1_LeaderStateFun_wf,
pv11_p1_LeaderState-classrel,
es-le_wf,
event-ordering+_subtype,
es-locl_wf,
es-E_wf,
all_wf,
bool_wf,
or_wf,
classrel_wf,
pv11_p1_propose'base_wf,
not_wf,
assert_wf,
pv11_p1_in_domain_wf,
exists_wf,
pv11_p1_adopted'base_wf,
pv11_p1_leq_bnum_wf,
pv11_p1_Ballot_Num_wf,
Id_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{}ldrs$_\mbackslash{}ff7\000Cbuid}$:Id {}\mrightarrow{} \mBbbZ{}.
\mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
((<s, c> \mmember{} snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e))))
{}\mRightarrow{} (\mexists{}e':E
((e' <loc e)
\mwedge{} (\mforall{}e'':E
((e' <loc e'')
{}\mRightarrow{} e'' \mleq{}loc e
{}\mRightarrow{} (<s, c> \mmember{} snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e'\000C'))))))
\mwedge{} ((<s, c> \mmember{} pv11\_p1\_propose'base(Cmd;f)(e')
\mwedge{} (\mneg{}\muparrow{}(pv11\_p1\_in\_domain(Cmd) s (snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid\mbackslash{}f\000Cf7d$;f;es;e')))))))
\mvee{} (\mexists{}pvals:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List
\mexists{}b:pv11\_p1\_Ballot\_Num()
(<fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e')), pvals> \mmember{}
pv11\_p1\_adopted'base(Cmd;f)(e')
\mwedge{} (<b, s, c> \mmember{} pvals)
\mwedge{} (\mforall{}b':pv11\_p1\_Ballot\_Num(). \mforall{}c':Cmd.
((<b', s, c'> \mmember{} pvals) {}\mRightarrow{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b\000C' b))))))))))
Date html generated:
2015_07_23-PM-04_47_33
Last ObjectModification:
2015_02_04-AM-08_21_48
Home
Index