lean_workbook_plus_54122

⚠️ 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.

The SOS (sum of squares) form of the inequality is $\sum (a-b)^2 [ (a+b)^2(a^2+b^2)-6a^2b^2-c^4] = \sum (a-b)^2 [ a^4+b^4+2ab(a^2+b^2-2ab)-c^4] = \sum (a-b)^2 [a^4+b^4+2ab(a-b)^2-c^4]$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_54122 :
  ∀ a b c : ℝ,
    (a - b) ^ 2 * ((a + b) ^ 2 * (a ^ 2 + b ^ 2) - 6 * a ^ 2 * b ^ 2 - c ^ 4) +
    (b - c) ^ 2 * ((b + c) ^ 2 * (b ^ 2 + c ^ 2) - 6 * b ^ 2 * c ^ 2 - a ^ 4) +
    (c - a) ^ 2 * ((c + a) ^ 2 * (c ^ 2 + a ^ 2) - 6 * c ^ 2 * a ^ 2 - b ^ 4) ≥ 0   :=  by sorry

The source fragment is an identity calculation and does not justify the added sign assertion.

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

Proposed corrected statement

State the cyclic algebraic identities actually displayed in the source, rather than inferring universal nonnegativity from them. If an inequality was intended, recover its variable-domain restrictions.

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.