Nuprl Lemma : pv11_p1_decision_from_p2a
∀[Cmd:ValueAllType]. ∀[f:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(f))]. ∀[accpts,ldrs:bag(Id)].
∀[ldrs_uid:Id ─→ ℤ]. ∀[reps:bag(Id)]. ∀[e:E]. ∀[k:ℤ]. ∀[v:Cmd].
∀a:Id
(pv11_p1_decision{i:l}(Cmd;f;accpts;ldrs;ldrs_uid;reps;es;e;k;v)
⇒ has-es-info-type(es;e;f;Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num())
⇒ a ↓∈ accpts
⇒ (↓∃e':E
(e' ≤loc e
∧ (k = (fst(snd(snd(msgval(e))))) ∈ ℤ)
∧ ((fst(snd(msgval(e)))) = (snd(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num())
∧ pv11_p1_p2a'send(Cmd;f) a <loc(e), fst(snd(msgval(e))), k, v> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f\000C)(e'))))
Proof
Definitions occuring in Statement :
pv11_p1_decision: pv11_p1_decision{i:l}(Cmd;f;accpts;ldrs;ldrs_uid;reps;es;e;k;v),
pv11_p1_p2a'send: pv11_p1_p2a'send(Cmd;f),
pv11_p1_main: pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
msg-interface: Interface,
es-info-body: msgval(e),
has-es-info-type: has-es-info-type(es;e;f;T),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
sq_stable__and,
equal_wf,
cons_wf_listp,
nil_wf,
listp_wf,
vatype_wf,
cons_wf,
list_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,
bag-member_wf,
has-es-info-type_wf,
pv11_p1_Ballot_Num_wf,
pv11_p1_decision_wf,
es-E_wf,
event-ordering+_subtype,
bag_wf,
Id_wf,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
pv11_p1_headers_type_wf,
set_wf,
valueall-type_wf,
make-Msg-as-mk-msg,
pv11_p1-decision,
bfalse_wf,
es-info-body_wf,
es-le_wf,
equal-wf-base-T,
int_subtype_base,
classrel_wf,
msg-interface_wf,
pv11_p1_main_wf,
pv11_p1_p2a'send_wf,
es-loc_wf,
es-le-loc,
and_wf,
pv11_p1-p2a,
subtype_base_sq
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[f:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(f))].
\mforall{}[accpts,ldrs:bag(Id)]. \mforall{}[ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}]. \mforall{}[reps:bag(Id)]. \mforall{}[e:E]. \mforall{}[k:\mBbbZ{}]\000C. \mforall{}[v:Cmd].
\mforall{}a:Id
(pv11\_p1\_decision\{i:l\}(Cmd;f;accpts;ldrs;ldrs$_{uid}$;reps;es;e;k;v)
{}\mRightarrow{} has-es-info-type(es;e;f;Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num())
{}\mRightarrow{} a \mdownarrow{}\mmember{} accpts
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E
(e' \mleq{}loc e
\mwedge{} (k = (fst(snd(snd(msgval(e))))))
\mwedge{} ((fst(snd(msgval(e)))) = (snd(snd(snd(msgval(e))))))
\mwedge{} pv11\_p1\_p2a'send(Cmd;f) a <loc(e), fst(snd(msgval(e))), k, v> \mmember{} pv11\_p1\_main(Cmd;accpts;\000Cldrs;ldrs$_{uid}$;reps;f)(
e'))))
Date html generated:
2015_07_23-PM-05_05_08
Last ObjectModification:
2015_02_04-AM-07_49_51
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