lean_workbook_plus_31130

⚠️ 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.

Let $a, b, c,$ be non-negative real numbers. Prove that \n

Why this node was retired

The posted statement is

theorem lean_workbook_plus_31130 : ∀ a b c : ℝ, (a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0) → 1 / (a ^ 2 + b ^ 2) + 1 / (b ^ 2 + c ^ 2) + 1 / (c ^ 2 + a ^ 2) ≥ 10 / (a + b + c) ^ 2   :=  by sorry

The target admits axis points at which a source denominator is zero; Lean assigns its reciprocal zero.

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

Proposed corrected statement

For nonnegative a,b,c require all three pairwise square sums to be positive (at least two variables positive) before the reciprocal inequality. Verify the repaired bound separately.

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.