Nuprl Lemma : consensus-ts4-estimate-domain
∀V:Type. ∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀a:{a:Id| (a ∈ A)} . ∀x:ts-reachable(consensus-ts4(V;A;W)). ∀i:ℤ.
((i ∈ fpf-domain(Estimate(x;a))) ⇒ (i ≤ Inning(x;a)))
Proof
Definitions occuring in Statement :
consensus-ts4: consensus-ts4(V;A;W),
cs-estimate: Estimate(s;a),
cs-inning: Inning(s;a),
fpf-domain: fpf-domain(f),
Id: Id,
l_member: (x ∈ l),
list: T List,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
ts-reachable: ts-reachable(ts)
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
uimplies: b supposing a,
guard: {T},
prop: ℙ,
ts-reachable: ts-reachable(ts),
consensus-ts4: consensus-ts4(V;A;W),
ts-type: ts-type(ts),
pi1: fst(t),
subtype_rel: A ⊆r B,
top: Top,
sq_stable: SqStable(P),
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
ts-init: ts-init(ts),
cs-inning: Inning(s;a),
cs-estimate: Estimate(s;a),
pi2: snd(t),
fpf-empty: ⊗,
fpf-domain: fpf-domain(f),
infix_ap: x f y,
consensus-state4: ConsensusState,
ts-rel: ts-rel(ts),
consensus-rel: CR[x,y],
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
Id: Id,
sq_type: SQType(T),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
fpf-single: x : v
Latex:
\mforall{}V:Type. \mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}a:\{a:Id| (a \mmember{} A)\} .
\mforall{}x:ts-reachable(consensus-ts4(V;A;W)). \mforall{}i:\mBbbZ{}.
((i \mmember{} fpf-domain(Estimate(x;a))) {}\mRightarrow{} (i \mleq{} Inning(x;a)))
Date html generated:
2016_05_16-AM-11_57_09
Last ObjectModification:
2016_01_17-PM-03_51_26
Theory : event-ordering
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