lean_workbook_plus_50967

⚠️ 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.

Given that $f(x) = -1$ for all $x \in \mathbb{R}$, show that it is a solution to the functional equation and comment on the positivity of the function.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_50967 (f : ℝ → ℝ) (hf: f = fun (x:ℝ) => -1) : (∀ x, f x = -1) ∧ (∀ x, 0 < f x)   :=  by sorry

The source asks to comment on positivity, not to assert a positive value.

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

Proposed corrected statement

Conclude ∀x,f(x)=−1 and ∀x,f(x)<0. Include the actual functional equation if the theorem is also meant to verify that f solves it.

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.