Nuprl Lemma : pv11_p1_ldr_mem_propose2
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀ldrs_uid:Id ─→ ℤ.
∀bnum1,bnum2:pv11_p1_Ballot_Num(). ∀active1,active2:𝔹. ∀proposals1,proposals2:(ℤ × Cmd) List. ∀s:ℤ. ∀c:Cmd.
((e1 <loc e2)
⇒ <s, c> ∈ pv11_p1_propose'base(Cmd;f)(e1)
⇒ <bnum1, active1, proposals1> ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e1)
⇒ <bnum2, active2, proposals2> ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e2)
⇒ (¬↑(pv11_p1_in_domain(Cmd) s proposals1))
⇒ (↑(pv11_p1_in_domain(Cmd) s proposals2)))
Proof
Definitions occuring in Statement :
pv11_p1_LeaderState: pv11_p1_LeaderState(Cmd;ldrs_uid;mf),
pv11_p1_propose'base: pv11_p1_propose'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,
list: T List,
vatype: ValueAllType,
assert: ↑b,
bool: 𝔹,
all: ∀x:A. B[x],
not: ¬A,
implies: 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_mem_propose,
disjoint-union-comb-classrel,
pv11_p1_propose'base_wf,
disjoint-union-comb_wf,
pv11_p1_adopted'base_wf,
pv11_p1_preempted'base_wf,
not_wf,
true_wf,
classrel_wf,
assert_witness,
pv11_p1_in_domain_wf,
assert_wf,
pv11_p1_LeaderState_wf,
es-locl_wf,
bool_wf,
pv11_p1_Ballot_Num_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{}bnum1,bnum2:pv11\_p1\_Ballot\_Num(). \mforall{}active1,active2:\mBbbB{}.
\mforall{}proposals1,proposals2:(\mBbbZ{} \mtimes{} Cmd) List. \mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
((e1 <loc e2)
{}\mRightarrow{} <s, c> \mmember{} pv11\_p1\_propose'base(Cmd;f)(e1)
{}\mRightarrow{} <bnum1, active1, proposals1> \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e1)
{}\mRightarrow{} <bnum2, active2, proposals2> \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e2)
{}\mRightarrow{} (\mneg{}\muparrow{}(pv11\_p1\_in\_domain(Cmd) s proposals1))
{}\mRightarrow{} (\muparrow{}(pv11\_p1\_in\_domain(Cmd) s proposals2)))
Date html generated:
2015_07_23-PM-04_45_24
Last ObjectModification:
2015_02_04-AM-07_19_07
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