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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