Nuprl Lemma : consensus-refinement1
∀[V:Type]. ts-refinement(consensus-ts1(V);consensus-ts2(V);λx.if cs-is-decided(x) then x else UNDECIDED fi )
Proof
Definitions occuring in Statement :
consensus-ts2: consensus-ts2(T),
cs-is-decided: cs-is-decided(x),
consensus-ts1: consensus-ts1(T),
cs-undecided: UNDECIDED,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type,
ts-refinement: ts-refinement(ts1;ts2;f)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
ts-refinement: ts-refinement(ts1;ts2;f),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
infix_ap: x f y,
ts-reachable: ts-reachable(ts),
subtype_rel: A ⊆r B,
consensus-ts2: consensus-ts2(T),
ts-init: ts-init(ts),
cs-is-decided: cs-is-decided(x),
pi2: snd(t),
pi1: fst(t),
cs-ambivalent: AMBIVALENT,
isl: isl(x),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
consensus-ts1: consensus-ts1(T),
ts-type: ts-type(ts),
consensus-state1: consensus-state1(V),
top: Top,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s],
cs-undecided: UNDECIDED,
ts-rel: ts-rel(ts),
cs-predecided: PREDECIDED[v],
cs-decided: Decided[v],
consensus-state2: consensus-state2(T),
ts-final: ts-final(ts)
Latex:
\mforall{}[V:Type]
ts-refinement(consensus-ts1(V);consensus-ts2(V);\mlambda{}x.if cs-is-decided(x) then x else UNDECIDED fi )
Date html generated:
2016_05_16-AM-11_47_48
Last ObjectModification:
2016_01_17-PM-03_53_14
Theory : event-ordering
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