lean_workbook_plus_36288

⚠️ 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.

With constant $m \in \mathbb{R}$ , find all functions $f:\mathbb{R} \to \mathbb{R}$ satisfy \n

Why this node was retired

The posted statement is

theorem lean_workbook_plus_36288 (m : ℝ): (∀ (f : ℝ → ℝ), (∀ x y, f (x + m * f (x * y)) = x * f x + m * x * f y) ↔ ∃ k:ℝ, ∀ x, f x = k * x)   :=  by sorry

For example m=0 admits only functions supported at x=1, not all linear functions; the full classification for other m is not established here.

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 classification of solutions for each real m and remove the assertion that every linear function works.

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.