Nuprl Lemma : consensus-ts4-inning-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.Inning(x;a) ≤ Inning(y;a))
Proof
Definitions occuring in Statement :
consensus-ts4: consensus-ts4(V;A;W),
cs-inning: Inning(s;a),
Id: Id,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
le: A ≤ B,
set: {x:A| B[x]} ,
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],
ts-stable-rel: ts-stable-rel(ts;x,y.R[x; y]),
implies: P ⇒ Q,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
consensus-ts4: consensus-ts4(V;A;W),
ts-rel: ts-rel(ts),
ts-type: ts-type(ts),
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
infix_ap: x f y,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
refl: Refl(T;x,y.E[x; y]),
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
trans: Trans(T;x,y.E[x; y]),
rel_implies: R1 => R2,
consensus-rel: CR[x,y],
Id: Id,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q)
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.Inning(x;a) \mleq{} Inning(y;a))
Date html generated:
2016_05_16-AM-11_56_45
Last ObjectModification:
2016_01_17-PM-03_52_26
Theory : event-ordering
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