Nuprl Lemma : new_23_sig_proposal_classrel2
∀[Cmd:ValueAllType]
∀propose:Atom List
∀[notify:Atom List]. ∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
∀es:EO+(Message(f)). ∀e:E.
∀[nc:ℤ × Cmd]
uiff(nc ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e);((header(e) = propose ∈ Name) ∧ nc = body(e))
∨ (has-es-info-type(es;e;f;ℤ × ℤ × Cmd × Id)
∧ (header(e) = ``new_23_sig vote`` ∈ Name)
∧ ((fst(nc)) = (fst(fst(fst(msgval(e))))) ∈ ℤ)
∧ ((snd(nc)) = (snd(fst(msgval(e)))) ∈ Cmd)))
Proof
Definitions occuring in Statement :
new_23_sig_Proposal: new_23_sig_Proposal(Cmd;notify;propose;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
equal-info-body: v = body(e),
es-info-body: msgval(e),
has-es-info-type: has-es-info-type(es;e;f;T),
es-header: header(e),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
name: Name,
cons: [a / b],
nil: [],
list: T List,
vatype: ValueAllType,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
or: P ∨ Q,
and: P ∧ Q,
product: x:A × B[x],
int: ℤ,
token: "$token",
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
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]),
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,
uimplies: b supposing a,
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),
decidable: Dec(P),
has-es-info-type: has-es-info-type(es;e;f;T),
pi1: fst(t),
pi2: snd(t),
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
equal-info-body: v = body(e),
es-info-type: es-info-type(es;e;f),
msg-type: msg-type(msg;f),
es-header: header(e),
new_23_sig_propose'base: new_23_sig_propose'base(Cmd;notify;propose;f),
encodes-msg-type: hdr encodes T,
new_23_sig_vote'base: new_23_sig_vote'base(Cmd;notify;propose;f),
list: T List,
new_23_sig_vote2prop: new_23_sig_vote2prop(Cmd),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Cmd:ValueAllType]
\mforall{}propose:Atom List
\mforall{}[notify:Atom List]. \mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)].
\mforall{}es:EO+(Message(f)). \mforall{}e:E.
\mforall{}[nc:\mBbbZ{} \mtimes{} Cmd]
uiff(nc \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e);((header(e) = propose)
\mwedge{} nc = body(e))
\mvee{} (has-es-info-type(es;e;f;\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd \mtimes{} Id)
\mwedge{} (header(e) = ``new\_23\_sig vote``)
\mwedge{} ((fst(nc)) = (fst(fst(fst(msgval(e))))))
\mwedge{} ((snd(nc)) = (snd(fst(msgval(e)))))))
Date html generated:
2016_05_17-PM-02_28_01
Last ObjectModification:
2016_01_18-AM-09_32_45
Theory : 2!3!consensus!with!signatures
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