lean_workbook_plus_8670

⚠️ 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.

Given the Fibonacci sequence $F_n$, prove that $F_n = c\alpha^n + d\beta^n$ where $\alpha = \frac{1+\sqrt{5}}{2}$, $\beta = \frac{1-\sqrt{5}}{2}$, and $c, d$ are constants.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_8670 (F : ℕ → ℝ) (h : F 0 = 1 ∧ F 1 = 1) : ∃ c d : ℝ, ∀ n : ℕ, F n = c * (1 + Real.sqrt 5) / 2 ^ n + d * (1 - Real.sqrt 5) / 2 ^ n   :=  by sorry

Restore the Fibonacci recurrence and parenthesize the full characteristic roots before exponentiation: F_n=c*((1+√5)/2)^n+d*((1−√5)/2)^n.

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 the Fibonacci recurrence and parenthesize the full characteristic roots before exponentiation: F_n=c*((1+√5)/2)^n+d*((1−√5)/2)^n.

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.