Nuprl Lemma : open-random-variable
∀p:FinProbSpace. ∀n:ℕ. ∀C:p-open(p). (λs.(C <n, s>) ∈ RandomVariable(p;n))
Proof
Definitions occuring in Statement :
p-open: p-open(p),
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
lambda: λx.A[x],
pair: <a, b>
Definitions unfolded in proof :
random-variable: RandomVariable(p;n),
p-outcome: Outcome,
all: ∀x:A. B[x],
member: t ∈ T,
p-open: p-open(p),
uall: ∀[x:A]. B[x],
nat: ℕ,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
int_seg_wf,
p-outcome_wf,
subtype_rel_set,
rationals_wf,
lelt_wf,
int-subtype-rationals,
p-open_wf,
nat_wf,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lambdaEquality,
applyEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
dependent_pairEquality,
functionEquality,
lemma_by_obid,
isectElimination,
natural_numberEquality,
intEquality,
independent_isectElimination
Latex:
\mforall{}p:FinProbSpace. \mforall{}n:\mBbbN{}. \mforall{}C:p-open(p). (\mlambda{}s.(C <n, s>) \mmember{} RandomVariable(p;n))
Date html generated:
2016_05_15-PM-11_48_54
Last ObjectModification:
2015_12_28-PM-07_14_44
Theory : randomness
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