Step
*
of Lemma
rv-unbounded_wf
∀[p:FinProbSpace]. ∀[f:ℕ ⟶ ℕ]. ∀[X:n:ℕ ⟶ RandomVariable(p;f[n])]. ((X[n]⟶∞ as n⟶∞) ∈ (ℕ ⟶ Outcome) ⟶ ℙ)
BY
{ (Auto
THEN Unfold `rv-unbounded` 0
THEN Auto
THEN Try ((Fold `p-outcome` 0 THEN Auto))
THEN Try (Unfold `p-outcome` 0)
THEN Try (Fold `random-variable` 0)
THEN Auto) }
Latex:
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{})
By
Latex:
(Auto
THEN Unfold `rv-unbounded` 0
THEN Auto
THEN Try ((Fold `p-outcome` 0 THEN Auto))
THEN Try (Unfold `p-outcome` 0)
THEN Try (Fold `random-variable` 0)
THEN Auto)
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