Nuprl Lemma : new_23_sig_quorum_inv_vote2
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e:E. ∀ni:ℤ × ℤ. ∀p:Cmd List × (Id List).
(p ∈ new_23_sig_QuorumState(Cmd;notify;propose;f) ni(e)
⇒ let cmds,locs = p
in no_repeats(Id;locs)
∧ (||locs|| = ||cmds|| ∈ ℤ)
∧ (∀i:ℕ||locs||
(↓∃e':E
((e' <loc e)
∧ <<ni, cmds[i]>, locs[i]> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(e')
∧ (∀e''∈[es-init(es;e);e').∀c:Cmd
(¬<<ni, c>, locs[i]> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(
e'')))))))
Proof
Definitions occuring in Statement :
new_23_sig_QuorumState: new_23_sig_QuorumState(Cmd;notify;propose;f),
new_23_sig_vote'base: new_23_sig_vote'base(Cmd;notify;propose;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-init: es-init(es;e),
es-closed-open-interval: [e;e'),
es-locl: (e <loc e'),
es-E: E,
Id: Id,
l_all: (∀x∈L.P[x]),
no_repeats: no_repeats(T;l),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
vatype: ValueAllType,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
spread: spread def,
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
int: ℤ,
atom: Atom,
equal: s = t ∈ T
Lemmas :
int_seg_wf,
length_wf,
name_wf,
new_23_sig_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
new_23_sig_headers_fun_wf,
cons_member,
cons_wf,
cons_wf_listp,
listp_wf,
nil_wf,
equal-wf-base,
list_subtype_base,
atom_subtype_base,
iff_weakening_equal,
name_eq_wf,
bool_wf,
eqtt_to_assert,
assert-name_eq,
sq_stable__no_repeats,
squash_wf,
true_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
classrel_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
list_wf,
Id_wf,
Memory1-memory-class1,
new_23_sig_add_to_quorum_wf,
new_23_sig_vote'base_wf,
Memory-loc-class-invariant-sv1,
no_repeats_wf,
all_wf,
exists_wf,
es-locl_wf,
select_wf,
sq_stable__le,
less_than_transitivity1,
le_weakening,
l_all_wf2,
es-closed-open-interval_wf,
es-init_wf,
not_wf,
single-bag_wf,
base-headers-msg-val-single-val,
subtype_rel_weakening,
ext-eq_weakening,
single-valued-bag-single,
bag-member-single,
length_of_nil_lemma,
stuck-spread,
base_wf,
no_repeats_nil,
less_than_irreflexivity,
bag-member_wf,
new_23_sig_newvote_wf,
length_of_cons_lemma,
no_repeats_cons,
productdeq_reduce_lemma,
intdeq_reduce_lemma,
assert_of_band2,
eq_int_wf,
assert_of_eq_int,
iff_transitivity,
assert_wf,
int_subtype_base,
iff_weakening_uiff,
assert_of_band,
bnot_wf,
deq-member_wf,
id-deq_wf,
assert_of_bnot,
assert-deq-member,
Memory-loc-class_wf,
new_23_sig_QuorumState_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
new_23_sig_headers_type_wf,
set_wf,
valueall-type_wf,
decidable__equal_int,
set_subtype_base,
lelt_wf,
new_23_sig_quorum_mem,
new_23_sig_QuorumStateFun_wf,
member-es-closed-open-interval,
new_23_sig_QuorumState-classrel,
pair-eta,
subtype_rel_product,
top_wf,
subtype_top,
subtract_wf,
decidable__le,
false_wf,
not-le-2,
not-equal-2,
add_functionality_wrt_le,
zero-add,
add-zero,
le-add-cancel,
condition-implies-le,
minus-one-mul,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
minus-zero,
decidable__lt,
less-iff-le,
length_cons,
non_neg_length,
length_wf_nat,
le_antisymmetry_iff,
le-add-cancel2,
select_cons_tl
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}notify,propose:Atom List. \mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).
\mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}ni:\mBbbZ{} \mtimes{} \mBbbZ{}. \mforall{}p:Cmd List \mtimes{} (Id List).
(p \mmember{} new\_23\_sig\_QuorumState(Cmd;notify;propose;f) ni(e)
{}\mRightarrow{} let cmds,locs = p
in no\_repeats(Id;locs)
\mwedge{} (||locs|| = ||cmds||)
\mwedge{} (\mforall{}i:\mBbbN{}||locs||
(\mdownarrow{}\mexists{}e':E
((e' <loc e)
\mwedge{} <<ni, cmds[i]>, locs[i]> \mmember{} new\_23\_sig\_vote'base(Cmd;notify;propose;f)(e')
\mwedge{} (\mforall{}e''\mmember{}[es-init(es;e);e').\mforall{}c:Cmd
(\mneg{}<<ni, c>, locs[i]> \mmember{}
new\_23\_sig\_vote'base(Cmd;notify;propose;f)(
e'')))))))
Date html generated:
2015_07_23-PM-03_57_15
Last ObjectModification:
2015_02_04-PM-01_55_40
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