lean_workbook_plus_79435

⚠️ 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 sequence of numbers is defined as follows: $a_1 = 1$, $a_2 = 2$, and for $n > 2$, $a_n = a_{n-1} + a_{n-2}$. What is the value of $a_6$?

Why this node was retired

The posted statement is

theorem lean_workbook_plus_79435 (a : ℕ → ℕ) (a1 : a 0 = 1) (a2 : a 1 = 2) (a_rec : ∀ n, n > 2 → a n = a (n-1) + a (n-2)) : a 6 = 8   :=  by sorry

One-based initial conditions were shifted without shifting recurrence scope; the inserted answer8 is wrong even for the source sequence.

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

Proposed corrected statement

Use a₁=1,a₂=2,aₙ=aₙ₋₁+aₙ₋₂ for n≥3 and prove a₆=13. In zero-based form use a₀=1,a₁=2 and the recurrence from n=2, and ask for a₅=13.

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.