Nuprl Lemma : pv11_p1_ldr_fun_mem_adopted
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀ldrs_uid:Id ─→ ℤ.
∀pvals:(pv11_p1_Ballot_Num() × ℤ × Cmd) List. ∀s:ℤ. ∀c:Cmd.
((e1 <loc e2)
⇒ <fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e1)), pvals> ∈ pv11_p1_adopted'base(Cmd;f)(e1)
⇒ ((↓(<s, c> ∈ snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e1)))))
∨ (∃b:pv11_p1_Ballot_Num(). (↓(<b, s, c> ∈ pvals))))
⇒ (↑(pv11_p1_in_domain(Cmd) s (snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e2)))))))
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_in_domain: pv11_p1_in_domain(Cmd),
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,
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],
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ
Lemmas :
disjoint-union-comb-classrel,
Message_wf,
pv11_p1_propose'base_wf,
disjoint-union-comb_wf,
pv11_p1_adopted'base_wf,
pv11_p1_preempted'base_wf,
pv11_p1_LeaderStateFun_wf,
bool_wf,
list_wf,
false_wf,
not_wf,
true_wf,
classrel_wf,
pair-eta,
subtype_rel_product,
pv11_p1_Ballot_Num_wf,
top_wf,
subtype_top,
pi2_wf,
sq_stable__assert,
pv11_p1_in_domain_wf,
pv11_p1_dummy_ballot_wf,
l_member_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e1,e2:E.
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}pvals:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List. \mforall{}s:\mBbbZ{}. \mforall{}c:Cm\000Cd.
((e1 <loc e2)
{}\mRightarrow{} <fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e1)), pvals> \mmember{} pv11\_p1\_ad\000Copted'base(Cmd;f)(e1)
{}\mRightarrow{} ((\mdownarrow{}(<s, c> \mmember{} snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e1)))))
\mvee{} (\mexists{}b:pv11\_p1\_Ballot\_Num(). (\mdownarrow{}(<b, s, c> \mmember{} pvals))))
{}\mRightarrow{} (\muparrow{}(pv11\_p1\_in\_domain(Cmd) s (snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}\mbackslash{}ff2\000C4;f;es;e2)))))))
Date html generated:
2015_07_23-PM-04_47_10
Last ObjectModification:
2015_01_29-AM-09_52_16
Home
Index