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
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
vatype: ValueAllType,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
squash: ↓T,
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
prop: ℙ
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:
2016_05_17-PM-02_15_08
Last ObjectModification:
2016_01_18-AM-09_32_05
Theory : 2!3!consensus!with!signatures
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