lean_workbook_plus_5821

⚠️ 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 $P(x)$ be the assertion $f(x)f(f(x)+\frac 1x)=1$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_5821 (f : ℝ → ℝ) (hf : ∀ x ≠ 0, f x * f (f x + 1/x) = 1) : ∀ x ≠ 0, f x = 1/x   :=  by sorry

The excerpt only defines an assertion; the target adds an unjustified reciprocal-function classification, refuted by f≡1.

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

Proposed corrected statement

Recover the original functional equation and domain; do not conclude f(x)=1/x from the displayed product relation alone.

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.