Nuprl Lemma : consensus-ts4-passed-stable
∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List]. ∀[a:{a:Id| (a ∈ A)} ]. ∀[i:ℤ].
ts-stable(consensus-ts4(V;A;W);s.by state s, a passed inning i without archiving a value)
Proof
Definitions occuring in Statement :
cs-passed: by state s, a passed inning i without archiving a value,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
ts-stable: ts-stable(ts;x.P[x])
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
ts-stable: ts-stable(ts;x.P[x]),
implies: P ⇒ Q,
cs-passed: by state s, a passed inning i without archiving a value,
and: P ∧ Q,
consensus-ts4: consensus-ts4(V;A;W),
ts-type: ts-type(ts),
pi1: fst(t),
uimplies: b supposing a,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
top: Top,
prop: ℙ,
ts-rel: ts-rel(ts),
pi2: snd(t),
infix_ap: x f y,
so_lambda: λ2x.t[x],
so_apply: x[s],
consensus-rel: CR[x,y],
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
Id: Id,
sq_type: SQType(T),
guard: {T},
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
true: True,
iff: P ⇐⇒ Q,
fpf-single: x : v,
fpf-domain: fpf-domain(f)
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{}[i:\mBbbZ{}].
ts-stable(consensus-ts4(V;A;W);s.by state s, a passed inning i without archiving a value)
Date html generated:
2016_05_16-AM-11_59_16
Last ObjectModification:
2016_01_17-PM-03_52_45
Theory : event-ordering
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