Nuprl Lemma : new_23_sig_vote_with_ballot_first-not
∀Cmd:ValueAllType. ∀propose,notify:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e:E. ∀n,r:ℤ.
((∃e'∈[es-init(es;e);e). ↑new_23_sig_vote_with_ballot_and_id(Cmd;notify;propose;f;es;e';n;r;snd(...)))) supposing
((¬↑new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es;e;n;r)) and
(↑new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;r)))
Proof
Definitions occuring in Statement :
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_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),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
es-info-body: msgval(e),
Message: Message(f),
event-ordering+: EO+(Info),
es-init: es-init(es;e),
es-closed-open-interval: [e;e'),
es-E: E,
l_exists: (∃x∈L. P[x]),
list: T List,
vatype: ValueAllType,
assert: ↑b,
uimplies: b supposing a,
pi2: snd(t),
all: ∀x:A. B[x],
not: ¬A,
int: ℤ,
atom: Atom
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
prop: ℙ,
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
l_all: (∀x∈L.P[x]),
and: P ∧ Q,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
iff: P ⇐⇒ Q,
name: Name,
new_23_sig_headers: new_23_sig_headers(notify;propose),
listp: A List+,
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
new_23_sig_headers_fun: new_23_sig_headers_fun(Cmd;notify;propose),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
sq_stable: SqStable(P),
cand: A c∧ B,
new_23_sig_headers_no_rep: new_23_sig_headers_no_rep(notify;propose),
squash: ↓T,
no_repeats: no_repeats(T;l),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
length: ||as||,
list_ind: list_ind,
cons: [a / b],
nil: [],
less_than: a < b,
true: True,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
select: L[n],
subtract: n - m,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
band: p ∧b q,
atom-deq: AtomDeq,
eq_atom: x =a y,
null: null(as),
new_23_sig_vote_with_ballot_first: new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es;e;n;r),
has-es-info-type: has-es-info-type(es;e;f;T),
pi2: snd(t)
Latex:
\mforall{}Cmd:ValueAllType. \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,r:\mBbbZ{}.
((\mexists{}e'\mmember{}[es-init(es;e);e). \muparrow{}...)) supposing
((\mneg{}\muparrow{}new\_23\_sig\_vote\_with\_ballot\_first(Cmd;notify;propose;f;es;e;n;r)) and
(\muparrow{}new\_23\_sig\_vote\_with\_ballot(Cmd;notify;propose;f;es;e;n;r)))
Date html generated:
2016_05_17-PM-02_32_55
Last ObjectModification:
2016_01_18-AM-09_30_22
Theory : 2!3!consensus!with!signatures
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