lean_workbook_plus_45256

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

And the unique solution $\boxed{f(x)=-x-1\quad\forall x\in\mathbb Z}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_45256 (f : ℤ → ℤ) (hf: f = fun x => x - f x - 1) : f = fun x => -x - 1   :=  by sorry

The imposed pointwise identity forces 2f(0)=−1 in ℤ and is inconsistent. The excerpt only states a purported answer and does not provide the original equation.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Recover the original functional equation on ℤ before asserting f(x)=−x−1. For the posted equation f(x)=x−f(x)−1 there is no integer-valued solution; this is the correct conclusion for that equation.

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.