Nuprl Lemma : new_23_sig_vote_with_ballot_and_id-if-snd
∀[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]. ∀[i:Id].
(↑new_23_sig_vote_with_ballot_and_id(Cmd;notify;propose;f;es;e;n;r;i)) supposing
(((snd(msgval(e))) = i ∈ Id) 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_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-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi2: snd(t),
int: ℤ,
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
name: Name,
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
listp: A List+,
implies: P ⇒ Q,
sq_stable: SqStable(P),
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
new_23_sig_headers: new_23_sig_headers(notify;propose),
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 ,
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),
false: False,
not: ¬A,
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),
has-es-info-type: has-es-info-type(es;e;f;T),
pi2: snd(t),
new_23_sig_vote_with_ballot: new_23_sig_vote_with_ballot(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),
pi1: fst(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{}].
\mforall{}[i:Id].
(\muparrow{}new\_23\_sig\_vote\_with\_ballot\_and\_id(Cmd;notify;propose;f;es;e;n;r;i)) supposing
(((snd(msgval(e))) = i) 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_00
Last ObjectModification:
2016_01_18-AM-09_30_59
Theory : 2!3!consensus!with!signatures
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