lean_workbook_plus_23316

⚠️ 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.

Your inequality is equivalent to the following: \n $\sum_{sym}(4a^7b+5a^6b^2-4a^5b^3-5a^4b^4+7a^6bc+12a^5b^2c-14a^4b^3c-5a^3b^3c^2)\geq0,$\nwhich obviously true.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_23316 :
  ∀ a b c : ℝ, (4 * a^7 * b + 5 * a^6 * b^2 - 4 * a^5 * b^3 - 5 * a^4 * b^4 + 7 * a^6 * b * c + 12 * a^5 * b^2 * c - 14 * a^4 * b^3 * c - 5 * a^3 * b^3 * c^2) + (4 * b^7 * c + 5 * b^6 * c^2 - 4 * b^5 * c^3 - 5 * b^4 * c^4 + 7 * b^6 * c * a + 12 * b^5 * c^2 * a - 14 * b^4 * c^3 * a - 5 * b^3 * c^3 * a^2) + (4 * c^7 * a + 5 * c^6 * a^2 - 4 * c^5 * a^3 - 5 * c^4 * a^4 + 7 * c^6 * a * b + 12 * c^5 * a^2 * b - 14 * c^4 * a^3 * b - 5 * c^3 * a^3 * b^2) ≥ 0   :=  by sorry

The source uses a symmetric sum, whereas the formal expression includes only three cyclic permutations.

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

Proposed corrected statement

Sum the polynomial over all six permutations of a,b,c, and recover the original sign hypotheses before asserting nonnegativity.

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.