Nuprl Lemma : pv11_p1_AcceptorState-classrel
∀[Cmd:ValueAllType]. ∀[ldrs_uid:Id ─→ ℤ]. ∀[mf:pv11_p1_headers_type{i:l}(Cmd)].
∀es:EO+(Message(mf)). ∀e:E. ∀v:pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List).
(v ∈ pv11_p1_AcceptorState(Cmd;ldrs_uid;mf)(e)
⇐⇒ v
= pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;mf;es;e)
∈ (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
Proof
Definitions occuring in Statement :
pv11_p1_AcceptorStateFun: pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;mf;es;e),
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-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Lemmas :
sq_stable__and,
equal_wf,
cons_wf_listp,
nil_wf,
listp_wf,
vatype_wf,
cons_wf,
equal-wf-T-base,
sq_stable__equal,
squash_wf,
int_seg_wf,
length_wf,
name_wf,
pv11_p1_headers_wf,
l_all_iff,
l_member_wf,
pv11_p1_headers_fun_wf,
cons_member,
equal-wf-base,
iff_weakening_equal,
classrel-classfun,
pv11_p1_AcceptorState-functional,
classrel_wf,
pv11_p1_AcceptorState_wf,
pv11_p1_AcceptorStateFun_wf,
pv11_p1_Ballot_Num_wf,
list_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
pv11_p1_headers_type_wf,
Id_wf,
set_wf,
valueall-type_wf
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}]. \mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd\000C)].
\mforall{}es:EO+(Message(mf)). \mforall{}e:E. \mforall{}v:pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List).
(v \mmember{} pv11\_p1\_AcceptorState(Cmd;ldrs$_{uid}$;mf)(e)
\mLeftarrow{}{}\mRightarrow{} v = pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;mf;es;e))
Date html generated:
2015_07_23-PM-04_12_58
Last ObjectModification:
2015_02_04-AM-07_24_11
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