Nuprl Lemma : consensus-ts4-archived-invariant
∀[V:Type]
∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List]. ∀[x:ts-reachable(consensus-ts4(V;A;W))]. ∀[i:ℤ]. ∀[v:V]. ∀[a:{a:Id|
(a ∈ A)} ]\000C.
∀[j:ℕi]. ∀[v':V]. v' = v ∈ V supposing in state x, inning j could commit v'
supposing by state x, a archived v in inning i
supposing ∀v1,v2:V. Dec(v1 = v2 ∈ V)
Proof
Definitions occuring in Statement :
cs-inning-committable: in state s, inning i could commit v ,
cs-archived: by state s, a archived v in inning i,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
ts-reachable: ts-reachable(ts),
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s],
ts-type: ts-type(ts),
pi1: fst(t),
consensus-ts4: consensus-ts4(V;A;W),
consensus-state4: ConsensusState,
ts-init: ts-init(ts),
ts-rel: ts-rel(ts),
pi2: snd(t),
cs-archived: by state s, a archived v in inning i,
cs-estimate: Estimate(s;a),
fpf-empty: ⊗,
fpf-domain: fpf-domain(f),
and: P ∧ Q,
not: ¬A,
false: False,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
consensus-rel: CR[x,y],
exists: ∃x:A. B[x],
squash: ↓T,
true: True,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
Id: Id,
sq_type: SQType(T),
cand: A c∧ B,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
fpf-single: x : v,
cs-inning-committable: in state s, inning i could commit v ,
cs-precondition: state s may consider v in inning i,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
nat: ℕ,
cs-not-completed: in state s, a has not completed inning i
Latex:
\mforall{}[V:Type]
\mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[x:ts-reachable(consensus-ts4(V;A;W))]. \mforall{}[i:\mBbbZ{}].
\mforall{}[v:V]. \mforall{}[a:\{a:Id| (a \mmember{} A)\} ].
\mforall{}[j:\mBbbN{}i]. \mforall{}[v':V]. v' = v supposing in state x, inning j could commit v'
supposing by state x, a archived v in inning i
supposing \mforall{}v1,v2:V. Dec(v1 = v2)
Date html generated:
2016_05_16-PM-00_09_20
Last ObjectModification:
2016_01_17-PM-04_02_55
Theory : event-ordering
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