lean_workbook_plus_19478

⚠️ 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 $f:Q->Q$ such that for all rational $x,y$ we have: $f(2xy+1/2)+f(x-y)=4f(x)f(y)+1/2$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_19478 (f : ℚ → ℚ) (h : ∀ x y : ℚ, f (2 * x * y + 1 / 2) + f (x - y) = 4 * f x * f y + 1 / 2) : ∃ a :ℚ, ∀ x : ℚ, f x = x * a   :=  by sorry

A quadratic functional-equation solution was incorrectly replaced by a linear-through-zero classification.

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

Proposed corrected statement

For f:ℚ→ℚ, prove the given functional equation holds for every x,y exactly when f(x)=x²+1/4 for every x.

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.