lean_workbook_plus_12327

⚠️ 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.

Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that $f(1)=1$ and for all $n \in \mathbb{N}$, $f(n+1) = \begin{cases} f(n) + 2, & \text{if } f(f(n) - n + 1) = n \\ f(n) + 1, & \text{otherwise} \end{cases}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_12327 (f : ℕ → ℕ) (hf: f 1 = 1) (hf2: ∀ n, f (n+1) = if f (f n - n + 1) = n then f n + 2 else f n + 1): ∀ n, f n = n   :=  by sorry

The complete corrected classification has not been established in this audit.

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 source task of determining functions satisfying the recurrence; remove the invented identity-function answer, which already disagrees at2.

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.