lean_workbook_plus_82347

⚠️ 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 $f: N \to N$ which satisfy. (1) if x<y then f(x)<f(y); (2) if f(yf(x))=x^{2}f(xy).

Why this node was retired

The posted statement is

theorem lean_workbook_plus_82347 : ∀ f : ℕ → ℕ, (∀ x y, x < y → f x < f y) ∧ (∀ x y, f (y * f x) = x^2 * f (x * y)) ↔ ∀ x, f x = x   :=  by sorry

The source asks for all solutions or a value; the stored theorem supplies an unsupported answer contradicted by an accepted disproof.

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

Proposed corrected statement

Find all strictly increasing f:ℕ→ℕ satisfying the given equation; remove the unsupported identity-function classification and prove both directions of the actual classification.

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.