Nuprl Lemma : new_23_sig_when_quorum_wf
∀[Cmd:ValueAllType]. ∀[cmdeq:EqDecider(Cmd)]. ∀[coeff,flrs:ℤ]. ∀[notify,propose:Atom List]. ∀[reps:bag(Id)].
∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
(new_23_sig_when_quorum(Cmd;cmdeq;coeff;flrs;notify;propose;reps;f) ∈ (ℤ × ℤ)
⟶ Id
⟶ (ℤ × ℤ × Cmd × Id)
⟶ (Cmd List × (Id List))
⟶ bag(Interface))
Proof
Definitions occuring in Statement :
new_23_sig_when_quorum: new_23_sig_when_quorum(Cmd;cmdeq;coeff;flrs;notify;propose;reps;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
msg-interface: Interface,
Id: Id,
list: T List,
deq: EqDecider(T),
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ,
atom: Atom,
bag: bag(T)
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[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]),
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),
new_23_sig_when_quorum: new_23_sig_when_quorum(Cmd;cmdeq;coeff;flrs;notify;propose;reps;f)
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[cmdeq:EqDecider(Cmd)]. \mforall{}[coeff,flrs:\mBbbZ{}]. \mforall{}[notify,propose:Atom List].
\mforall{}[reps:bag(Id)]. \mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)].
(new\_23\_sig\_when\_quorum(Cmd;cmdeq;coeff;flrs;notify;propose;reps;f) \mmember{} (\mBbbZ{} \mtimes{} \mBbbZ{})
{}\mrightarrow{} Id
{}\mrightarrow{} (\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd \mtimes{} Id)
{}\mrightarrow{} (Cmd List \mtimes{} (Id List))
{}\mrightarrow{} bag(Interface))
Date html generated:
2016_05_17-PM-02_02_53
Last ObjectModification:
2016_01_18-AM-09_35_19
Theory : 2!3!consensus!with!signatures
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