Step
*
of Lemma
rcos-seq-converges
rcos-seq(n)↓ as n→∞
BY
{ (InstLemma `increasing-sequence-converges` [⌜λn.rcos-seq(n)⌝]⋅ THEN All Reduce THEN Auto) }
1
∃c:{2...}
∃m:ℕ+
((∀n:ℕ+. ((rcos-seq(n + 1) - rcos-seq(n)) ≤ ((r1/r(c)) * (rcos-seq(n) - rcos-seq(n - 1)))))
∧ ((r(c) * (rcos-seq(1) - rcos-seq(0))/r(c - 1)) ≤ (r1/r(m))))
Latex:
Latex:
rcos-seq(n)\mdownarrow{} as n\mrightarrow{}\minfty{}
By
Latex:
(InstLemma `increasing-sequence-converges` [\mkleeneopen{}\mlambda{}n.rcos-seq(n)\mkleeneclose{}]\mcdot{} THEN All Reduce THEN Auto)
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