lean_workbook_plus_70021

⚠️ 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.

Prove that $\sqrt{x+1}-\sqrt{4x-1}=\sqrt{x-1}$ has no real solution.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_70021 : ¬ (∃ x : ℝ, (Real.sqrt (x + 1) - Real.sqrt (4 * x - 1) = Real.sqrt (x - 1)))   :=  by sorry

Totalized square roots admit negative radicands; the ordinary radical domain is absent.

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

Proposed corrected statement

Prove no real x≥1 satisfies√(x+1)−√(4x−1)=√(x−1). This is exactly the ordinary real-radical domain.

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.