Nuprl Lemma : new_23_sig_voter_start
∀[Cmd:ValueAllType]. ∀[propose,notify:Atom List]. ∀[slots:set-sig{i:l}(ℤ)].
∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[n:ℤ]. ∀[c:Cmd].
(<n, c> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e)
⇒ (↓∃e':E
∃c':Cmd
(e' ≤loc e
∧ <n, c'> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e')
∧ (¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e'))))))
Proof
Definitions occuring in Statement :
new_23_sig_ReplicaStateFun: new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e),
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),
set-sig-member: set-sig-member(s),
set-sig: set-sig{i:l}(Item),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
list: T List,
vatype: ValueAllType,
assert: ↑b,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
atom: Atom
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
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+,
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,
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),
strongwellfounded: SWellFounded(R[x; y]),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P)
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[propose,notify:Atom List]. \mforall{}[slots:set-sig\{i:l\}(\mBbbZ{})].
\mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E]. \mforall{}[n:\mBbbZ{}].
\mforall{}[c:Cmd].
(<n, c> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e)
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E
\mexists{}c':Cmd
(e' \mleq{}loc e
\mwedge{} <n, c'> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e')
\mwedge{} (\mneg{}\muparrow{}(set-sig-member(slots) n
new\_23\_sig\_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e'))))))
Date html generated:
2016_05_17-PM-02_35_11
Last ObjectModification:
2016_01_18-AM-09_29_28
Theory : 2!3!consensus!with!signatures
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