lean_workbook_plus_48407

⚠️ 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.

Another elementary example with $f_n(x) =|x|, |x| \geq 1/n, f_n(x) = nx^2/2, |x| \leq 1/n$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_48407 (f : ℕ → ℝ → ℝ) (hf: ∀ n, ∀ x, f n x = if abs x ≥ 1/n then abs x else n * x ^ 2 / 2) : ∃ x, ¬ ∃ n, ∀ y, f n y = f x y   :=  by sorry

For every index x, n=x makes the row equality true. The source only defines an example and its piecewise boundary convention also needs clarification.

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 property this sequence was intended to illustrate; remove the impossible claim that some indexed function has no equal indexed function.

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.