lean_workbook_plus_28245

⚠️ 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.

By Cauchy-Schwarz inequality (CS): $(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2})(\frac{a^2}{c^2}+\frac{b^2}{a^2}+\frac{c^2}{b^2}) \ge (\frac {a^2} {bc} +\frac {b^2} {ca} +\frac {c^2} {ab})^2 = (a^3+b^3+c^3)^2 \ge \frac{(a^3+b^3+c^3)^2+9}{2}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_28245 :  ∀ a b c : ℝ, (a^2 / b^2 + b^2 / c^2 + c^2 / a^2) * (a^2 / c^2 + b^2 / a^2 + c^2 / b^2) ≥ (a^3 + b^3 + c^3)^2 ∧ (a^3 + b^3 + c^3)^2 ≥ (a^3 + b^3 + c^3)^2 + 9 / 2   :=  by sorry

The last source denominator 2 should divide the entire sum, but the formal target adds 9/2 to the unchanged left expression, an impossibility.

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 ((a³+b³+c³)²+9)/2 and recover the missing normalization, such as abc=1 if that is the original context; prove the intervening Cauchy–Schwarz step under its actual hypotheses.

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.