Nuprl Lemma : committed-inning0-reachable
∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List].
∀[v:V]. (λa.<0, 0 : v> ∈ ts-reachable(consensus-ts4(V;A;W))) supposing ||W|| ≥ 1
Proof
Definitions occuring in Statement :
consensus-ts4: consensus-ts4(V;A;W),
fpf-single: x : v,
Id: Id,
l_member: (x ∈ l),
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
member: t ∈ T,
set: {x:A| B[x]} ,
lambda: λx.A[x],
pair: <a, b>,
natural_number: $n,
universe: Type,
ts-reachable: ts-reachable(ts)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
consensus-ts4: consensus-ts4(V;A;W),
ts-reachable: ts-reachable(ts),
ts-init: ts-init(ts),
ts-rel: ts-rel(ts),
ts-type: ts-type(ts),
pi1: fst(t),
pi2: snd(t),
subtype_rel: A ⊆r B,
consensus-state4: ConsensusState,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
l_all: (∀x∈L.P[x]),
l_contains: A ⊆ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
le: A ≤ B,
eq_id: a = b,
decidable: Dec(P),
bor: p ∨bq,
consensus-rel: CR[x,y],
infix_ap: x f y,
cs-inning: Inning(s;a),
cs-estimate: Estimate(s;a),
cand: A c∧ B,
fpf-empty: ⊗,
fpf-domain: fpf-domain(f),
true: True,
sq_stable: SqStable(P),
squash: ↓T,
fpf-single: x : v,
cs-precondition: state s may consider v in inning i,
cons: [a / b],
less_than': less_than'(a;b),
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List].
\mforall{}[v:V]. (\mlambda{}a.ɘ, 0 : v> \mmember{} ts-reachable(consensus-ts4(V;A;W))) supposing ||W|| \mgeq{} 1
Date html generated:
2016_05_16-PM-00_07_46
Last ObjectModification:
2016_01_17-PM-03_58_32
Theory : event-ordering
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