Nuprl Lemma : new_23_sig_quorum_inv_vote2_fun
∀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.
(no_repeats(Id;snd(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e)))
∧ (||snd(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))||
= ||fst(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))||
∈ ℤ)
∧ (∀i:ℕ||snd(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))||
(↓∃e':E
((e' <loc e)
∧ <<ni, fst(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]>
, snd(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]
> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(e')
∧ (∀e''∈[es-init(es;e);e').∀c:Cmd
(¬<<ni, c>, snd(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]> ∈
new_23_sig_vote'base(Cmd;notify;propose;f)(e'')))))))
Proof
Definitions occuring in Statement :
new_23_sig_QuorumStateFun: new_23_sig_QuorumStateFun(Cmd;notify;propose;f;x;es;e),
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,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
and: P ∧ Q,
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,
Id_wf,
new_23_sig_quorum_inv_vote2,
new_23_sig_QuorumStateFun_wf,
new_23_sig_QuorumState-classrel,
new_23_sig_quorum_invariant_fun,
pair-eta,
subtype_rel_product,
list_wf,
top_wf,
subtype_top,
no_repeats_witness,
es-E_wf,
event-ordering+_subtype,
event-ordering+_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{}e:E. \mforall{}ni:\mBbbZ{} \mtimes{} \mBbbZ{}.
(no\_repeats(Id;snd(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e)))
\mwedge{} (||snd(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))||
= ||fst(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))||)
\mwedge{} (\mforall{}i:\mBbbN{}||snd(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))||
(\mdownarrow{}\mexists{}e':E
((e' <loc e)
\mwedge{} <<ni, fst(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]>
, snd(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[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>, snd(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;ni;es;e))[i]> \mmember{}
new\_23\_sig\_vote'base(Cmd;notify;propose;f)(e'')))))))
Date html generated:
2015_07_23-PM-03_57_17
Last ObjectModification:
2015_02_04-PM-01_48_16
Home
Index