lean_workbook_plus_60031

⚠️ 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.

Prove that $a_n = \frac{1}{n}$ for all $n$ in the naturals using the given recursive relation $a_{n+1} = \frac{1}{1+\frac{1}{a_n}}$ and initial condition $a_{1} = 1$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_60031 (a : ℕ → ℝ) (a1 : a 0 = 1) (a_rec : ∀ n, a (n + 1) = 1 / (1 + 1 / a n)) : ∀ n, a n = 1 / n   :=  by sorry

The initial value was shifted from index1 to0 without changing the formula.

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

Proposed corrected statement

With a₀=1 and the posted recurrence prove a_n=1/(n+1). Alternatively use a₁=1, recurrence only for n≥1, and conclude a_n=1/n for n≥1.

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.