lean_workbook_plus_43681

⚠️ 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 the inequality $\frac{1}{{{b^2} + bc + {c^2}}} + \frac{1}{{{c^2} + ca + {a^2}}} + \frac{1}{{{a^2} + ab + {b^2}}} \ge \frac{9}{{{{(a + b + c)}^2}}}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_43681 : ∀ a b c : ℝ, (1 / (b ^ 2 + b * c + c ^ 2) + 1 / (c ^ 2 + c * a + a ^ 2) + 1 / (a ^ 2 + a * b + b ^ 2)) ≥ 9 / (a + b + c) ^ 2   :=  by sorry

The accepted zero tuple in two coordinates makes one denominator undefined.

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 a,b,c>0 or the source’s exact nonzero/sign assumptions for the ordinary reciprocal inequality.

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.