lean_workbook_plus_11116

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

If $b_n=\frac{1}{a_n}$ , then $b_1=1,b_{n+1}=b_n+\frac{1}{b_n}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_11116 {b : ℕ → ℝ} (a : ℕ → ℝ) (hb : b = fun n ↦ 1 / a n) : b 1 = 1 ∧ ∀ n, b (n + 1) = b n + 1 / b n   :=  by sorry

The source gives a transformation of an absent recurrence; the inferred original recurrence should be confirmed against that source.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Restore a₁=1, aₙ≠0, and the original recurrence for a, namely a_(n+1)=a_n/(1+a_n²) for n≥1, before deriving the displayed reciprocal recurrence.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.