lean_workbook_plus_62770

⚠️ 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.

1. shur $a^3+b^3+c^3+3abc\geq a^2b+b^2a+c^2b+cb^2+c^2a+a^2c$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_62770 : ∀ a b c : ℝ, a^3 + b^3 + c^3 + 3 * a * b * c ≥ a^2 * b + b^2 * a + c^2 * b + b * c^2 + c^2 * a + a * c^2   :=  by sorry

The symmetric cubic sum was expanded with duplicated terms and missing monomials; Schur also requires nonnegative variables.

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 a,b,c≥0 prove∑a³+3abc≥a²b+a²c+b²a+b²c+c²a+c²b, preserving all six distinct terms.

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.