lean_workbook_plus_20280

⚠️ 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 $a,b,c \ge 0$. Prove $(ab+bc+ca)(\frac{1}{(b+c)^{2}}+\frac{1}{(a+c)^{2}}+\frac{1}{(a+b)^{2}}) \ge \frac{9}{4}+\frac{1}{16}(\frac{(a-b)^{2}}{(a+b)^{2}}+\frac{(a-c)^{2}}{(a+c)^{2}}+\frac{(b-c)^{2}}{(b+c)^{2}})$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_20280 : ∀ a b c : ℝ, (a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0 → (a * b + b * c + c * a) * (1 / (b + c) ^ 2 + 1 / (a + c) ^ 2 + 1 / (a + b) ^ 2) ≥ 9 / 4 + 1 / 16 * (a - b) ^ 2 / (a + b) ^ 2 + (a - c) ^ 2 / (a + c) ^ 2 + (b - c) ^ 2 / (b + c) ^ 2)   :=  by sorry

Apply1/16 to the entire parenthesized sum of three fractions, and exclude zero pair-sum denominators.

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

Proposed corrected statement

Apply1/16 to the entire parenthesized sum of three fractions, and exclude zero pair-sum denominators.

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.