Nuprl Lemma : new_23_sig_quorum_mem
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e1,e2:E. ∀ni:ℤ × ℤ. ∀s1,s2:Cmd List × (Id List). ∀v:ℤ × ℤ × Cmd × Id.
((e1 <loc e2)
⇒ v ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(e1)
⇒ s1 ∈ new_23_sig_QuorumState(Cmd;notify;propose;f) ni(e1)
⇒ s2 ∈ new_23_sig_QuorumState(Cmd;notify;propose;f) ni(e2)
⇒ let cmds1,locs1 = s1
in let cmds2,locs2 = s2
in let x,i = v
in let ni',c = x
in (ni = ni' ∈ (ℤ × ℤ)) ⇒ ((i ∈ locs2) ∧ ((¬(i ∈ locs1)) ⇒ (c ∈ cmds2))))
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-locl: (e <loc e'),
es-E: E,
Id: Id,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
all: ∀x:A. B[x],
not: ¬A,
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 :
new_23_sig_newvote_wf,
bool_wf,
eqtt_to_assert,
cons_member,
l_member_wf,
Id_wf,
not_wf,
equal-wf-base,
int_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
productdeq_reduce_lemma,
intdeq_reduce_lemma,
iff_transitivity,
assert_wf,
eq_int_wf,
assert_of_eq_int,
bnot_wf,
deq-member_wf,
id-deq_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_bnot,
assert-deq-member,
not_over_and,
decidable__cand,
decidable__equal_int,
decidable__int_equal,
or_wf,
decidable__l_member,
decidable__equal_Id,
neg_assert_of_eq_int,
base-headers-msg-val-single-val,
cons_wf_listp,
cons_wf,
nil_wf,
listp_wf,
subtype_rel_weakening,
ext-eq_weakening,
single-valued-bag-single,
list_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,e2:E. \mforall{}ni:\mBbbZ{} \mtimes{} \mBbbZ{}. \mforall{}s1,s2:Cmd List \mtimes{} (Id List). \mforall{}v:\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd \mtimes{} Id.
((e1 <loc e2)
{}\mRightarrow{} v \mmember{} new\_23\_sig\_vote'base(Cmd;notify;propose;f)(e1)
{}\mRightarrow{} s1 \mmember{} new\_23\_sig\_QuorumState(Cmd;notify;propose;f) ni(e1)
{}\mRightarrow{} s2 \mmember{} new\_23\_sig\_QuorumState(Cmd;notify;propose;f) ni(e2)
{}\mRightarrow{} let cmds1,locs1 = s1
in let cmds2,locs2 = s2
in let x,i = v
in let ni',c = x
in (ni = ni') {}\mRightarrow{} ((i \mmember{} locs2) \mwedge{} ((\mneg{}(i \mmember{} locs1)) {}\mRightarrow{} (c \mmember{} cmds2))))
Date html generated:
2015_07_23-PM-03_57_10
Last ObjectModification:
2015_01_29-AM-08_52_58
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