Nuprl Lemma : filter-vote-with-ballot-lemma
∀Cmd:{T:Type| valueall-type(T)} . ∀propose,notify:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose).
∀es:EO+(Message(f)). ∀e:E. ∀n:ℤ. ∀e':E.
  (filter(λa.new_23_sig_vote_with_ballot_first_alt(Cmd;notify;propose;f;es;e;e';n;0;a);[e, e']) 
  ~ filter(λe'.new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es.e;e';n;0);[e, e']))
Proof
Definitions occuring in Statement : 
new_23_sig_vote_with_ballot_first_alt: new_23_sig_vote_with_ballot_first_alt(Cmd;notify;propose;f;es;e;e';n;r;a)
, 
new_23_sig_vote_with_ballot_first: new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es;e;n;r)
, 
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose)
, 
Message: Message(f)
, 
eo-forward: eo.e
, 
event-ordering+: EO+(Info)
, 
es-interval: [e, e']
, 
es-E: E
, 
filter: filter(P;l)
, 
list: T List
, 
valueall-type: valueall-type(T)
, 
all: ∀x:A. B[x]
, 
set: {x:A| B[x]} 
, 
lambda: λx.A[x]
, 
natural_number: $n
, 
int: ℤ
, 
atom: Atom
, 
universe: Type
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
vatype: ValueAllType
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
sq_stable: SqStable(P)
, 
squash: ↓T
, 
new_23_sig_vote_with_ballot_first_alt: new_23_sig_vote_with_ballot_first_alt(Cmd;notify;propose;f;es;e;e';n;r;a)
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
band: p ∧b q
, 
ifthenelse: if b then t else f fi 
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
or: P ∨ Q
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
rev_implies: P 
⇐ Q
, 
has-es-info-type: has-es-info-type(es;e;f;T)
, 
pi2: snd(t)
, 
rev_uimplies: rev_uimplies(P;Q)
, 
not: ¬A
, 
deq: EqDecider(T)
, 
cand: A c∧ B
, 
eq_id: a = b
, 
Id: Id
, 
new_23_sig_vote_with_ballot_and_id: new_23_sig_vote_with_ballot_and_id(Cmd;notify;propose;f;es;e;n;r;i)
, 
new_23_sig_vote_with_ballot: new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;r)
, 
pi1: fst(t)
Latex:
\mforall{}Cmd:\{T:Type|  valueall-type(T)\}  .  \mforall{}propose,notify:Atom  List.
\mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).  \mforall{}es:EO+(Message(f)).  \mforall{}e:E.  \mforall{}n:\mBbbZ{}.  \mforall{}e':E.
    (filter(\mlambda{}a.new\_23\_sig\_vote\_with\_ballot\_first\_alt(Cmd;notify;propose;f;es;e;e';n;0;a);[e,  e']) 
    \msim{}  filter(\mlambda{}e'.new\_23\_sig\_vote\_with\_ballot\_first(Cmd;notify;propose;f;es.e;e';n;0);[e,  e']))
Date html generated:
2016_05_17-PM-02_35_34
Last ObjectModification:
2016_01_18-AM-09_30_15
Theory : 2!3!consensus!with!signatures
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