lean_workbook_plus_15621

⚠️ 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 $f \colon \mathbb{N}\times\mathbb{N} \to \mathbb{N}$ which satisfy\n(a) $f(n,n) = n \forall n \in \mathbb{N}$\n(b) $f(n,m) = f(m,n) \forall n,m \in \mathbb{N}$\n(c) $\frac{f(m,n+m)}{f(m,n)} = \frac{m+n}{n} \forall m,n \in \mathbb{N}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_15621 : ∀ f : ℕ → ℕ → ℕ, (∀ n, f n n = n) ∧ (∀ n m, f n m = f m n) ∧ (∀ m n, (f m (n + m) / f m n) = (m + n) / n) ↔ ∀ n m, f n m = m * (n / m)   :=  by sorry

The full classification is not established by this audit; zero-domain and division choices must match the original source.

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 positive natural inputs, compute the ratios in ℚ, and restore the source task of finding all such functions instead of the nonsymmetric proposed answer.

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.