Step
*
of Lemma
converges-absolutely-converges
∀x:ℕ ⟶ ℝ. (converges-absolutely(n.x[n])
⇒ Σn.x[n]↓)
BY
{ (Unfold `converges-absolutely` 0
THEN Auto
THEN ((InstLemma `comparison-test` [⌜λ2n.|x[n]|⌝])⋅ THENA Auto)
THEN (BHyp (-1))
THEN Auto) }
Latex:
Latex:
\mforall{}x:\mBbbN{} {}\mrightarrow{} \mBbbR{}. (converges-absolutely(n.x[n]) {}\mRightarrow{} \mSigma{}n.x[n]\mdownarrow{})
By
Latex:
(Unfold `converges-absolutely` 0
THEN Auto
THEN ((InstLemma `comparison-test` [\mkleeneopen{}\mlambda{}\msubtwo{}n.|x[n]|\mkleeneclose{}])\mcdot{} THENA Auto)
THEN (BHyp (-1))
THEN Auto)
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