Nuprl Lemma : pv11_p1_A3
∀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(). ∀accepted1,accepted2:(pv11_p1_Ballot_Num() × ℤ × Cmd) List.
((e1 <loc e2)
⇒ <bnum1, accepted1> ∈ pv11_p1_AcceptorState(Cmd;ldrs_uid;f)(e1)
⇒ <bnum2, accepted2> ∈ pv11_p1_AcceptorState(Cmd;ldrs_uid;f)(e2)
⇒ (∀pv:pv11_p1_Ballot_Num() × ℤ × Cmd. ((pv ∈ accepted1) ⇒ (pv ∈ accepted2))))
Proof
Definitions occuring in Statement :
pv11_p1_AcceptorState: pv11_p1_AcceptorState(Cmd;ldrs_uid;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,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
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,
classrel_wf,
pv11_p1_AcceptorState_wf,
es-locl_wf,
list_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,
pv11_p1_inc_acc,
iseg_member
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{}accepted1,accepted2:(\000Cpv11\_p1\_Ballot\_Num()
\mtimes{} \mBbbZ{}
\mtimes{} Cmd) List.
((e1 <loc e2)
{}\mRightarrow{} <bnum1, accepted1> \mmember{} pv11\_p1\_AcceptorState(Cmd;ldrs$_{uid}$;f)(e1)
{}\mRightarrow{} <bnum2, accepted2> \mmember{} pv11\_p1\_AcceptorState(Cmd;ldrs$_{uid}$;f)(e2)
{}\mRightarrow{} (\mforall{}pv:pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd. ((pv \mmember{} accepted1) {}\mRightarrow{} (pv \mmember{} accepted2))))
Date html generated:
2015_07_23-PM-04_49_55
Last ObjectModification:
2015_02_04-AM-07_58_15
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