Nuprl Lemma : consensus-ts4-estimate-rel
∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List]. ∀[a:{a:Id| (a ∈ A)} ].
ts-stable-rel(consensus-ts4(V;A;W);x,y.Estimate(x;a) ⊆ Estimate(y;a))
Proof
Definitions occuring in Statement :
consensus-ts4: consensus-ts4(V;A;W),
cs-estimate: Estimate(s;a),
fpf-sub: f ⊆ g,
Id: Id,
l_member: (x ∈ l),
list: T List,
int-deq: IntDeq,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
ts-stable-rel: ts-stable-rel(ts;x,y.R[x; y])
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
ts-type: ts-type(ts),
pi1: fst(t),
consensus-ts4: consensus-ts4(V;A;W),
consensus-state4: ConsensusState,
so_apply: x[s1;s2],
implies: P ⇒ Q,
refl: Refl(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
prop: ℙ,
ts-rel: ts-rel(ts),
pi2: snd(t),
rel_implies: R1 => R2,
infix_ap: x f y,
ts-stable-rel: ts-stable-rel(ts;x,y.R[x; y]),
uimplies: b supposing a,
consensus-rel: CR[x,y],
exists: ∃x:A. B[x],
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
Id: Id,
sq_type: SQType(T),
guard: {T}
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[a:\{a:Id| (a \mmember{} A)\} ].
ts-stable-rel(consensus-ts4(V;A;W);x,y.Estimate(x;a) \msubseteq{} Estimate(y;a))
Date html generated:
2016_05_16-AM-11_56_54
Last ObjectModification:
2015_12_29-PM-01_20_29
Theory : event-ordering
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