Nuprl Lemma : pv11_p1_unique_adopted
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀accpts,ldrs:bag(Id).
∀ldrs_uid:Id ─→ ℤ. ∀reps:bag(Id). ∀bnum:pv11_p1_Ballot_Num(). ∀pvals1,pvals2:(pv11_p1_Ballot_Num() × ℤ × Cmd) List.
∀proposals1,proposals2:(ℤ × Cmd) List. ∀b1,b2:𝔹.
(pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)
⇒ <bnum, pvals1> ∈ pv11_p1_adopted'base(Cmd;f)(e1)
⇒ <bnum, pvals2> ∈ pv11_p1_adopted'base(Cmd;f)(e2)
⇒ <bnum, b1, proposals1> ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e1)
⇒ <bnum, b2, proposals2> ∈ pv11_p1_LeaderState(Cmd;ldrs_uid;f)(e2)
⇒ e1 ≤loc e2
⇒ (pvals1 = pvals2 ∈ ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
Proof
Definitions occuring in Statement :
pv11_p1_message-constraint: pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; mf; es),
pv11_p1_LeaderState: pv11_p1_LeaderState(Cmd;ldrs_uid;mf),
pv11_p1_adopted'base: pv11_p1_adopted'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),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
bool: 𝔹,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
classrel_wf,
Message_wf,
pv11_p1_adopted'base_wf,
base-headers-msg-val-single-val,
cons_wf_listp,
cons_wf,
nil_wf,
listp_wf,
subtype_rel_weakening,
ext-eq_weakening,
and_wf,
equal_wf,
pi2_wf,
list_wf,
base-noloc-classrel-make-Msg2,
hdrmkmsg_lemma,
cons_member,
name_wf,
l_member_wf,
equal-wf-base,
msg-header_wf,
pv11_p1_headers_no_inputs_wf,
squash_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
es-causl_wf,
msg-interface_wf,
pv11_p1_main_wf,
make-msg-interface_wf,
es-loc_wf,
msg-authentic_wf,
es-info_wf,
pv11_p1-adopted,
length_wf_nat,
nat_wf,
es-locl-trichotomy,
Id_wf,
pv11_p1_init_ballot_num_wf,
pv11_p1_ScoutStateFun_wf,
true_wf,
pv11_p1_Ballot_Num_wf,
subtype_rel_dep_function,
vatype_wf,
event-ordering+_wf,
pv11_p1_headers_type_wf,
bag_wf,
pv11_p1_adopted'send_wf,
eclass2-classrel,
eclass1_wf,
pv11_p1_p1b'base_wf,
pv11_p1_scout_output_wf,
pv11_p1_ScoutState_wf,
es-info-body_wf,
bag-member_wf,
eclass1-classrel,
base-noloc-classrel,
pv11_p1_ScoutState-classrel,
pair-eta,
subtype_rel_product,
top_wf,
subtype_top,
pv11_p1_eq_bnums_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
eqtt_to_assert,
pv11_p1_eq_bnums-assert,
lt_int_wf,
bag-size_wf,
pv11_p1_threshold_wf,
less_than_wf,
assert_of_lt_int,
bag-member-single,
iff_weakening_equal,
le_int_wf,
le_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
bag-member-empty-iff,
less_than_transitivity1,
less_than_irreflexivity,
iff_transitivity,
not_wf,
iff_weakening_uiff,
assert_of_bnot,
pv11_p1_preempted'send_wf,
subtype_base_sq,
union_subtype_base,
unit_wf2,
product_subtype_base,
int_subtype_base,
atom2_subtype_base,
unit_subtype_base,
pv11_p1_ldr_fun_pos,
pv11_p1_lt_bnum_trans2,
pv11_p1_LeaderStateFun_wf,
pv11_p1_lt_bnum_wf,
assert_of_bor,
eq_int_wf,
assert_of_eq_int,
btrue_wf,
isl_wf,
bfalse_wf,
btrue_neq_bfalse,
subtype_rel_sum,
or_wf,
less-iff-le,
le_antisymmetry_iff,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
assert_of_band,
es-le-loc,
eo-forward_wf,
member-eo-forward-E,
pv11_p1_upd_bnum_wf,
pv11_p1_ldr_mem_preempted,
valueall-type_wf,
pv11_p1_LeaderState-classrel,
disjoint-union-comb-classrel,
pv11_p1_propose'base_wf,
disjoint-union-comb_wf,
pv11_p1_preempted'base_wf,
false_wf,
add-swap,
add-mul-special,
zero-mul,
event_ordering_wf,
no-classrel-in-interval_wf,
eclass_wf,
eclass2_wf,
list_subtype_base,
atom_subtype_base,
subtype_rel_wf,
eo-forward-loc,
subtype_rel_transitivity,
es-info-type_wf,
es-le_transitivity,
es-le_weakening_eq,
pi1_wf_top,
pv11_p1_leq_bnum_wf,
pv11_p1_lt_bnum_upd,
pv11_p1_lt_bnum_implies_not2
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e1,e2:E.
\mforall{}accpts,ldrs:bag(Id). \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}reps:bag(Id). \mforall{}bnum:pv11\_p1\_Ballot\000C\_Num().
\mforall{}pvals1,pvals2:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List. \mforall{}proposals1,proposals2:(\mBbbZ{} \mtimes{} Cmd) List.
\mforall{}b1,b2:\mBbbB{}.
(pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\mbackslash{}\000Cff24; reps; f; es)
{}\mRightarrow{} <bnum, pvals1> \mmember{} pv11\_p1\_adopted'base(Cmd;f)(e1)
{}\mRightarrow{} <bnum, pvals2> \mmember{} pv11\_p1\_adopted'base(Cmd;f)(e2)
{}\mRightarrow{} <bnum, b1, proposals1> \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e1)
{}\mRightarrow{} <bnum, b2, proposals2> \mmember{} pv11\_p1\_LeaderState(Cmd;ldrs$_{uid}$;f)(e2)
{}\mRightarrow{} e1 \mleq{}loc e2
{}\mRightarrow{} (pvals1 = pvals2))
Date html generated:
2015_07_23-PM-04_48_20
Last ObjectModification:
2015_02_04-AM-08_22_04
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