lean_workbook_plus_34904

⚠️ 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 continuous functions $f:\mathbb{R}\rightarrow \mathbb{R}$ that satisfy the condition: $xf(x^3)+f(1-x^2)=-x^{10}+x^6-2x \quad \forall x \in \mathbb{R}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_34904 (f : ℝ → ℝ) (hf: Continuous f) (hx: ∀ x : ℝ, x * f (x^3) + f (1 - x^2) = -x^10 + x^6 - 2 * x) : ∀ x : ℝ, f x = -x^7 + x^3 - 1   :=  by sorry

The accepted counterexample does not alone establish the full solution family.

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 finding functions satisfying the stated equation and remove the invented formula; f(x)=−x³+3x−2 is a valid candidate to check in the corrected 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.