lean_workbook_plus_1833

⚠️ 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.

Given the expanded form of the inequality after homogenization: $14[4;1;1]+10[3;2;1]+6[2;2;2] \geq 9[4;2;0]+18[3;3;0]$, find a method to prove it using AM-GM inequality.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_1833 : ∀ a b c : ℝ, (14 * (a ^ 4 * b + a ^ 4 * c + b ^ 4 * c + b ^ 4 * a + c ^ 4 * a + c ^ 4 * b) + 10 * (a ^ 3 * b ^ 2 + a ^ 3 * c ^ 2 + b ^ 3 * c ^ 2 + b ^ 3 * a ^ 2 + c ^ 3 * a ^ 2 + c ^ 3 * b ^ 2) + 6 * (a ^ 2 * b ^ 2 * c ^ 2) ≥ 9 * (a ^ 4 * b ^ 2 + a ^ 4 * c ^ 2 + b ^ 4 * c ^ 2 + b ^ 4 * a ^ 2 + c ^ 4 * a ^ 2 + c ^ 4 * b ^ 2) + 18 * (a ^ 3 * b ^ 3 + a ^ 3 * c ^ 3 + b ^ 3 * c ^ 3))   :=  by sorry

The bracket exponent triples were translated into monomials missing factors, destroying homogeneity; the bracket convention and sign domain are absent.

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

Proposed corrected statement

Define[p;q;r] as the intended symmetric sum of degree p+q+r in nonnegative a,b,c, including multiplicity convention. Restore all degree6 monomials in[4;1;1],[3;2;1],[2;2;2] and verify the source inequality.

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.