lean_workbook_plus_58875

⚠️ 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 $P(x,y)$ be the assertion $f(x+y)(f(x^2)-f(xy)+f(y)^2)=x^3-f(y)^3$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_58875 (f : ℤ → ℤ) (hf: f = fun x ↦ x) : ∀ x y, f (x + y) * (f (x ^ 2) - f (x * y) + f (y) ^ 2) = x ^ 3 - f (y) ^ 3   :=  by sorry

The source only defines the functional assertion P(x,y); the target inserts f=id, which fails because the polynomial factor gives x³+y³ rather than x³−y³.

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 full original functional-equation problem containing P(x,y):f(x+y)(f(x²)−f(xy)+f(y)²)=x³−f(y)³. The excerpt alone does not justify assuming f=id; recover the intended domain and full quantifiers before classifying solutions.

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.