Nuprl Lemma : pv11_p1_ldr_active_fun
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀ldrs_uid:Id ─→ ℤ.
((↑(fst(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e)))))
⇒ (↓∃e':E
∃pvals:(pv11_p1_Ballot_Num() × ℤ × Cmd) List
((e' <loc e)
∧ <fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e)), pvals> ∈ pv11_p1_adopted'base(Cmd;f)(e')
∧ ((fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e)))
= (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e')))
∈ pv11_p1_Ballot_Num()))))
Proof
Definitions occuring in Statement :
pv11_p1_LeaderStateFun: pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_adopted'base: pv11_p1_adopted'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-locl: (e <loc e'),
es-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
assert: ↑b,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ 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,
list_wf,
pv11_p1_ldr_active2,
pv11_p1_LeaderStateFun_wf,
pv11_p1_LeaderState-classrel,
pair-eta,
bool_wf,
subtype_rel_product,
pv11_p1_Ballot_Num_wf,
top_wf,
subtype_top,
es-locl_wf,
classrel_wf,
pv11_p1_adopted'base_wf,
exists_wf,
assert_wf,
Id_wf,
es-E_wf,
event-ordering+_subtype,
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{}.
((\muparrow{}(fst(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e)))))
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E
\mexists{}pvals:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List
((e' <loc e)
\mwedge{} <fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e)), pvals> \mmember{}
pv11\_p1\_adopted'base(Cmd;f)(e')
\mwedge{} ((fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e)))
= (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e')))))))
Date html generated:
2015_07_23-PM-04_45_44
Last ObjectModification:
2015_02_04-AM-08_26_11
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