Nuprl Lemma : pv11_p1_ldr_fun_mem_propose
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀ldrs_uid:Id ─→ ℤ.
∀p:ℤ × Cmd + pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List) + pv11_p1_Ballot_Num().
((e1 <loc e2)
⇒ p ∈ pv11_p1_propose'base(Cmd;f) (+) pv11_p1_adopted'base(Cmd;f) (+) pv11_p1_preempted'base(Cmd;f)(e1)
⇒ case p
of inl(x) =>
(¬↑(pv11_p1_in_domain(Cmd) (fst(x)) (snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e1))))))
⇒ (↑(pv11_p1_in_domain(Cmd) (fst(x)) (snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e2))))))
| inr(x) =>
True)
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_preempted'base: pv11_p1_preempted'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),
disjoint-union-comb: X (+) Y,
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],
not: ¬A,
implies: P ⇒ Q,
true: True,
apply: f a,
function: x:A ─→ B[x],
product: x:A × B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
union: left + right,
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,
pv11_p1_ldr_mem_propose,
pv11_p1_LeaderStateFun_wf,
pv11_p1_LeaderState-classrel,
pair-eta,
bool_wf,
list_wf,
subtype_rel_product,
pv11_p1_Ballot_Num_wf,
top_wf,
subtype_top,
not_wf,
assert_wf,
pv11_p1_in_domain_wf,
classrel_wf,
disjoint-union-comb_wf,
pv11_p1_propose'base_wf,
pv11_p1_adopted'base_wf,
pv11_p1_preempted'base_wf,
es-locl_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{}e1,e2:E.
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}p:\mBbbZ{} \mtimes{} Cmd + pv11\_p1\_Ballot\_Num()
\mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List) + pv11\_p1\_Ballot\_Num().
((e1 <loc e2)
{}\mRightarrow{} p \mmember{}
pv11\_p1\_propose'base(Cmd;f) (+) pv11\_p1\_adopted'base(Cmd;f) (+) pv11\_p1\_preempted'base(Cmd;f)(
e1)
{}\mRightarrow{} case p
of inl(x) =>
(\mneg{}\muparrow{}(pv11\_p1\_in\_domain(Cmd) (fst(x)) (snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid\000C}$;f;es;e1))))))
{}\mRightarrow{} (\muparrow{}(pv11\_p1\_in\_domain(Cmd) (fst(x))
(snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e2))))))
| inr(x) =>
True)
Date html generated:
2015_07_23-PM-04_45_27
Last ObjectModification:
2015_02_04-AM-07_19_02
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