lean_workbook_plus_79708

⚠️ 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.

Let $v_n = \dfrac{u_{n + 1}}{u_n}, \forall n \in \mathbb{N}$ then: $v_1 = 2, v_2 = 12, v_{n + 2} = 6v_{n + 1} - 8v_n$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_79708  (u : ℕ → ℝ)
  (h₀ : u 1 = 2)
  (h₁ : u 2 = 12)
  (h₂ : ∀ n, u (n + 2) = 6 * u (n + 1) - 8 * u n) :
  ∀ n, u (n + 1) / u n = if n = 0 then 2 else if n = 1 then 12 else 6 * (u (n + 1) / u n) - 8 * (u n / u (n - 1))   :=  by sorry

The excerpt supplies only the derived ratio sequence, not the original u recurrence.

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

Proposed corrected statement

Define v(n)=u(n+1)/u(n), require the relevant u values nonzero, and impose v(1)=2,v(2)=12 and v(n+2)=6v(n+1)−8v(n) on v, not on u. Restore any original equations on u needed to derive these facts.

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.