Nuprl Lemma : pv11_p1_ldr_ord
∀Cmd:ValueAllType. ∀ldrs_uid:Id ─→ ℤ. ∀mf:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(mf)). ∀e1,e2:E.
∀zs,z:pv11_p1_Ballot_Num() × 𝔹 × ((ℤ × Cmd) List).
((e1 <loc e2)
⇒ zs ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;mf)(e1)
⇒ z ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;mf)(e2)
⇒ let bnum1,active1,proposals1 = zs in
let bnum2,active2,proposals2 = z in
↑(pv11_p1_leq_bnum(ldrs_uid) bnum1 bnum2))
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_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
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,
list: T List,
vatype: ValueAllType,
assert: ↑b,
bool: 𝔹,
spreadn: spread3,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
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,
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-trans-refl,
assert_wf,
pv11_p1_leq_bnum_wf,
disjoint-union-tr_wf,
single-bag_wf,
disjoint-union-comb_wf,
assert_of_bor,
lt_int_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
le_int_wf,
le_weakening,
less_than_wf,
assert_of_lt_int,
iff_transitivity,
int_subtype_base,
le_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_le_int,
or_wf,
subtype_base_sq,
decidable__lt,
false_wf,
less-iff-le,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
le_transitivity,
sq_stable__assert,
disj_un_tr_ap_inl_lemma,
disj_un_tr_ap_inr_lemma,
pv11_p1_eq_bnums-assert,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
pv11_p1_lt_bnum_wf,
es-loc_wf,
assert_elim,
isl_wf,
unit_wf2,
bfalse_wf,
btrue_neq_bfalse,
pv11_p1_is_bnum_wf,
not_over_and,
decidable__assert,
disjoint-union-comb-single-val,
base-headers-msg-val-single-val,
subtype_rel_weakening,
ext-eq_weakening,
base-disjoint-classrel,
not_wf,
name_eq_wf,
bnot_wf,
assert-name_eq,
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,
es-le_weakening,
pv11_p1_LeaderState_wf,
es-locl_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
pv11_p1_headers_type_wf,
Id_wf,
set_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}mf:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}e\000Cs:EO+(Message(mf)).
\mforall{}e1,e2:E. \mforall{}zs,z:pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbB{} \mtimes{} ((\mBbbZ{} \mtimes{} Cmd) List).
((e1 <loc e2)
{}\mRightarrow{} zs \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;mf)(e1)
{}\mRightarrow{} z \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;mf)(e2)
{}\mRightarrow{} let bnum1,active1,proposals1 = zs in
let bnum2,active2,proposals2 = z in
\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) bnum1 bnum2))
Date html generated:
2015_07_23-PM-04_33_19
Last ObjectModification:
2015_02_04-AM-07_26_04
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