Nuprl Lemma : pv11_p1_ldr_state_fun_eq
∀[Cmd:ValueAllType]. ∀[f:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[ldrs_uid:Id ─→ ℤ].
(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;e)
= if first(e) then pv11_p1_init_leader(Cmd) loc(e)
if pred(e) ∈b pv11_p1_propose'base(Cmd;f)
then pv11_p1_on_propose(Cmd) loc(e) pv11_p1_propose'base(Cmd;f)@pred(e)
pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;pred(e))
if pred(e) ∈b pv11_p1_adopted'base(Cmd;f)
then pv11_p1_when_adopted(Cmd;ldrs_uid) loc(e) pv11_p1_adopted'base(Cmd;f)@pred(e)
pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;pred(e))
if pred(e) ∈b pv11_p1_preempted'base(Cmd;f)
then pv11_p1_when_preempted(Cmd;ldrs_uid) loc(e) pv11_p1_preempted'base(Cmd;f)@pred(e)
pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;pred(e))
else pv11_p1_LeaderStateFun(Cmd;ldrs_uid;f;es;pred(e))
fi
∈ (pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List)))
Proof
Definitions occuring in Statement :
pv11_p1_LeaderStateFun: pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_when_preempted: pv11_p1_when_preempted(Cmd;ldrs_uid),
pv11_p1_when_adopted: pv11_p1_when_adopted(Cmd;ldrs_uid),
pv11_p1_on_propose: pv11_p1_on_propose(Cmd),
pv11_p1_init_leader: pv11_p1_init_leader(Cmd),
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_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Message: Message(f),
classfun-res: X@e,
member-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
ifthenelse: if b then t else f fi ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
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_Ballot_Num_wf,
list_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,
bool_wf,
pv11_p1_init_leader_wf,
pv11_p1_on_propose_wf,
pv11_p1_propose'base_wf,
pv11_p1_when_adopted_wf,
pv11_p1_adopted'base_wf,
pv11_p1_when_preempted_wf,
pv11_p1_preempted'base_wf,
base-headers-msg-val-single-val,
subtype_rel_weakening,
ext-eq_weakening,
base-disjoint-classrel,
iff_transitivity,
not_wf,
assert_wf,
name_eq_wf,
bnot_wf,
assert-name_eq,
iff_weakening_uiff,
assert_of_bnot,
sq_stable__encodes-msg-type,
l_all_fwd,
equal-wf-T-base,
es-first_wf2,
eqtt_to_assert,
es-loc_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
member-eclass_wf,
es-pred_wf,
classfun-res_wf,
classfun_wf,
memory-class3_wf,
memory-class3-fun-eq,
memory-class3-functional
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[f:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E].
\mforall{}[ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}].
(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;e)
= if first(e) then pv11\_p1\_init\_leader(Cmd) loc(e)
if pred(e) \mmember{}\msubb{} pv11\_p1\_propose'base(Cmd;f)
then pv11\_p1\_on\_propose(Cmd) loc(e) pv11\_p1\_propose'base(Cmd;f)@pred(e)
pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;pred(e))
if pred(e) \mmember{}\msubb{} pv11\_p1\_adopted'base(Cmd;f)
then pv11\_p1\_when\_adopted(Cmd;ldrs$_{uid}$) loc(e) pv11\_p1\_adopted'base(Cm\000Cd;f)@pred(e)
pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;pred(e))
if pred(e) \mmember{}\msubb{} pv11\_p1\_preempted'base(Cmd;f)
then pv11\_p1\_when\_preempted(Cmd;ldrs$_{uid}$) loc(e) pv11\_p1\_preempted'bas\000Ce(Cmd;f)@pred(e)
pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;pred(e))
else pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;f;es;pred(e))
fi )
Date html generated:
2015_07_23-PM-04_46_37
Last ObjectModification:
2015_02_04-AM-08_24_27
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