Nuprl Lemma : new_23_sig_quorum_invariant_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))
Proof
Definitions occuring in Statement :
new_23_sig_QuorumStateFun: new_23_sig_QuorumStateFun(Cmd;notify;propose;f;x;es;e),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
Message: Message(f),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
no_repeats: no_repeats(T;l),
length: ||as||,
list: T List,
vatype: ValueAllType,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
and: P ∧ Q,
product: x:A × B[x],
int: ℤ,
atom: Atom,
equal: s = t ∈ T
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,
cand: A c∧ B,
subtype_rel: A ⊆r B,
vatype: ValueAllType,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
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{}.
(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))||))
Date html generated:
2016_05_17-PM-02_14_59
Last ObjectModification:
2015_12_29-PM-08_06_45
Theory : 2!3!consensus!with!signatures
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