Nuprl Lemma : rv-unbounded_wf
∀[p:FinProbSpace]. ∀[f:ℕ ⟶ ℕ]. ∀[X:n:ℕ ⟶ RandomVariable(p;f[n])].  ((X[n]⟶∞ as n⟶∞) ∈ (ℕ ⟶ Outcome) ⟶ ℙ)
Proof
Definitions occuring in Statement : 
rv-unbounded: (X[n]⟶∞ as n⟶∞)
, 
random-variable: RandomVariable(p;n)
, 
p-outcome: Outcome
, 
finite-prob-space: FinProbSpace
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
rv-unbounded: (X[n]⟶∞ as n⟶∞)
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
nat: ℕ
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
finite-prob-space: FinProbSpace
, 
uimplies: b supposing a
, 
le: A ≤ B
, 
and: P ∧ Q
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
all: ∀x:A. B[x]
, 
p-outcome: Outcome
Lemmas referenced : 
all_wf, 
rationals_wf, 
exists_wf, 
nat_wf, 
le_wf, 
qle_wf, 
subtype_rel_dep_function, 
p-outcome_wf, 
int_seg_wf, 
length_wf, 
int_seg_subtype_nat, 
false_wf, 
random-variable_wf, 
finite-prob-space_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lambdaEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
sqequalRule, 
because_Cache, 
functionEquality, 
setElimination, 
rename, 
hypothesisEquality, 
applyEquality, 
natural_numberEquality, 
independent_isectElimination, 
independent_pairFormation, 
lambdaFormation, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality
Latex:
\mforall{}[p:FinProbSpace].  \mforall{}[f:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}].  \mforall{}[X:n:\mBbbN{}  {}\mrightarrow{}  RandomVariable(p;f[n])].
    ((X[n]{}\mrightarrow{}\minfty{}  as  n{}\mrightarrow{}\minfty{})  \mmember{}  (\mBbbN{}  {}\mrightarrow{}  Outcome)  {}\mrightarrow{}  \mBbbP{})
Date html generated:
2016_05_15-PM-11_50_39
Last ObjectModification:
2015_12_28-PM-07_14_38
Theory : randomness
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