Nuprl Lemma : new_23_sig_quorum_inv_vote_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. ∀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')))
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-locl: (e <loc e'),
es-E: E,
Id: Id,
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],
squash: ↓T,
and: P ∧ Q,
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
int: ℤ,
atom: Atom
Lemmas :
new_23_sig_quorum_inv_vote,
new_23_sig_QuorumState-classrel,
pair-eta,
new_23_sig_QuorumStateFun_wf,
subtype_rel_product,
top_wf,
subtype_top,
int_seg_wf,
length_wf,
Id_wf,
list_wf,
es-E_wf,
event-ordering+_subtype,
Message_wf,
subtype_rel_dep_function,
name_wf,
vatype_wf,
event-ordering+_wf,
new_23_sig_headers_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{}.
\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')))
Date html generated:
2015_07_23-PM-03_57_05
Last ObjectModification:
2015_01_29-AM-08_49_34
Home
Index