Nuprl Lemma : fresh-inning-reachable
∀[V:Type]
∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀ws:{a:Id| (a ∈ A)} List. ∀x:ConsensusState. ∀i:ℤ.
((ws ∈ W)
⇒ x ((λx,y. CR(in ws)[x, y] )^*) (λa.<if a ∈b ws then i else Inning(x;a) fi , Estimate(x;a)>)
supposing (∀a∈ws.Inning(x;a) < i))
Proof
Definitions occuring in Statement :
consensus-rel-mod: CR(in ws)[x, y] ,
cs-estimate: Estimate(s;a),
cs-inning: Inning(s;a),
consensus-state4: ConsensusState,
id-deq: IdDeq,
Id: Id,
l_all: (∀x∈L.P[x]),
l_member: (x ∈ l),
deq-member: x ∈b L,
list: T List,
rel_star: R^*,
ifthenelse: if b then t else f fi ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
lambda: λx.A[x],
pair: <a, b>,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
l_all: (∀x∈L.P[x]),
prop: ℙ,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
deq-member: x ∈b L,
bfalse: ff,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
consensus-state4: ConsensusState,
cs-inning: Inning(s;a),
cs-estimate: Estimate(s;a),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
cand: A c∧ B,
infix_ap: x f y,
pi2: snd(t),
label: ...$L... t,
true: True,
Id: Id,
nat: ℕ,
ge: i ≥ j ,
pi1: fst(t),
l_member: (x ∈ l),
le: A ≤ B,
consensus-rel-mod: CR(in ws)[x, y] ,
subtract: n - m
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}ws:\{a:Id| (a \mmember{} A)\} List. \mforall{}x:ConsensusState. \mforall{}i:\mBbbZ{}.
((ws \mmember{} W)
{}\mRightarrow{} x
((\mlambda{}x,y. CR(in ws)[x, y] )\^{}*)
(\mlambda{}a.<if a \mmember{}\msubb{} ws then i else Inning(x;a) fi , Estimate(x;a)>)
supposing (\mforall{}a\mmember{}ws.Inning(x;a) < i))
Date html generated:
2016_05_16-PM-00_16_56
Last ObjectModification:
2016_01_17-PM-04_03_54
Theory : event-ordering
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