lean_workbook_plus_37651

⚠️ 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.

$a_{n}<(\frac{5-\sqrt{5}}{10})(\frac{1+\sqrt{5}}{2})^{n}+(\frac{5+\sqrt{5}}{10})(\frac{1+\sqrt{5}}{2})^{n}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_37651 (n : ℕ) (a : ℕ → ℝ) (h : ∀ n, a n = (5 - Real.sqrt 5) / 10 * (1 + Real.sqrt 5) / 2 ^ n + (5 + Real.sqrt 5) / 10 * (1 + Real.sqrt 5) / 2 ^ n) : a n < (5 - Real.sqrt 5) / 10 * (1 + Real.sqrt 5) / 2 ^ n + (5 + Real.sqrt 5) / 10 * (1 + Real.sqrt 5) / 2 ^ n   :=  by sorry

The target assumes a_n equals the very bound it asks to be strictly below; the power parentheses are also wrong.

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

Proposed corrected statement

Recover the actual sequence recurrence and initial values, then use powers((1+√5)/2)^n, with the entire base parenthesized. Do not define a_n to equal an alleged strict upper bound.

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.