lean_workbook_plus_39295

⚠️ 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 functions $f: (0,\infty)\rightarrow (0,\infty)$ such that $f(x+\sqrt{x}) \leq x \leq f(x)+\sqrt{f(x)}$ for all $x \in (0,\infty)$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_39295 (f : ℝ → ℝ) (hf: ∀ x > 0, f (x + Real.sqrt x) ≤ x ∧ x ≤ f x + Real.sqrt (f x)) : ∀ x > 0, f x = x   :=  by sorry

A complete uniqueness proof was not checked in this audit.

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

Proposed corrected statement

Restore the function-classification problem instead of f(x)=x; the function f(t)=((√(4t+1)−1)/2)² is a valid candidate that the corrected answer must include.

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.