Nuprl Lemma : pv11_p1_ldr_loc_bnum
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀ldrs_uid:Id ─→ ℤ.
∀v:pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List).
(v ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e)
⇒ let bnum,active,proposals = v in
∃n:ℤ. (bnum = (pv11_p1_mk_bnum() n loc(e)) ∈ pv11_p1_Ballot_Num()))
Proof
Definitions occuring in Statement :
pv11_p1_LeaderState: pv11_p1_LeaderState(Cmd;ldrs_uid;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_mk_bnum: pv11_p1_mk_bnum(),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
bool: 𝔹,
spreadn: spread3,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
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,
list_wf,
classrel_wf,
squash_wf,
true_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
pv11_p1_Ballot_Num_wf,
bool_wf,
Memory3-memory-class3,
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,
Memory-loc-class-invariant-sv1,
exists_wf,
pv11_p1_mk_bnum_wf,
es-loc_wf,
disjoint-union-tr_wf,
single-bag_wf,
Id_wf,
disjoint-union-comb_wf,
disjoint-union-comb-single-val,
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,
valueall-type_wf,
equal-wf-T-base,
disjoint-classrel-symm,
disjoint-union-comb-disjoint-classrel,
single-valued-bag-single,
bag-member-single,
pair-eta,
member_wf,
bag-member_wf,
disj_un_tr_ap_inl_lemma,
disj_un_tr_ap_inr_lemma,
subtype_base_sq,
union_subtype_base,
product_subtype_base,
int_subtype_base,
atom2_subtype_base,
unit_subtype_base,
pv11_p1_eq_bnums_wf,
eqtt_to_assert,
pv11_p1_eq_bnums-assert,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
subtype_rel_sum,
assert_of_bor,
lt_int_wf,
eq_int_wf,
assert_of_eq_int,
assert_of_lt_int,
less_than_wf,
assert_of_band,
or_wf,
and_wf,
assert_elim,
isl_wf,
unit_wf2,
bfalse_wf,
btrue_neq_bfalse,
Memory-loc-class_wf,
es-locl_wf,
pv11_p1_LeaderState_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
pv11_p1_headers_type_wf,
set_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}ldrs$_\mbackslash{}ff7\000Cbuid}$:Id {}\mrightarrow{} \mBbbZ{}.
\mforall{}v:pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbB{} \mtimes{} ((\mBbbZ{} \mtimes{} Cmd) List).
(v \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e)
{}\mRightarrow{} let bnum,active,proposals = v in
\mexists{}n:\mBbbZ{}. (bnum = (pv11\_p1\_mk\_bnum() n loc(e))))
Date html generated:
2015_07_23-PM-04_45_10
Last ObjectModification:
2015_02_04-AM-07_21_48
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