Nuprl Lemma : new_23_sig_quorum_invariant
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e1:E. ∀ni:ℤ × ℤ. ∀z:Cmd List × (Id List).
(z ∈ new_23_sig_QuorumState(Cmd;notify;propose;f) ni(e1)
⇒ let cmds,locs = z
in no_repeats(Id;locs) ∧ (||locs|| = ||cmds|| ∈ ℤ))
Proof
Definitions occuring in Statement :
new_23_sig_QuorumState: new_23_sig_QuorumState(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-E: E,
Id: Id,
no_repeats: no_repeats(T;l),
length: ||as||,
list: T List,
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
spread: spread def,
product: x:A × B[x],
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,
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,
no_repeats_nil,
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,
not_wf,
assert_of_bnot,
assert-deq-member,
Memory-loc-class_wf,
es-locl_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
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{}e1:E. \mforall{}ni:\mBbbZ{} \mtimes{} \mBbbZ{}. \mforall{}z:Cmd List \mtimes{} (Id List).
(z \mmember{} new\_23\_sig\_QuorumState(Cmd;notify;propose;f) ni(e1)
{}\mRightarrow{} let cmds,locs = z
in no\_repeats(Id;locs) \mwedge{} (||locs|| = ||cmds||))
Date html generated:
2015_07_23-PM-03_50_52
Last ObjectModification:
2015_02_04-PM-01_59_10
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