lean_workbook_plus_7678

⚠️ 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.

prove $(6,2,0)+(4,4,0)+(6,1,1)+(3,3,2)+2(4,3,1)\ge6(4,2,2)$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_7678 : (6, 2, 0) + (4, 4, 0) + (6, 1, 1) + (3, 3, 2) + 2 * (4, 3, 1) ≥ 6 * (4, 2, 2)   :=  by sorry

The source exponent-triple notation for symmetric polynomial sums was interpreted as literal vectors with coordinatewise order.

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)=∑sym aᵖbᑫcʳ for specified nonnegative a,b,c, then formulate the displayed symmetric-sum inequality using that definition; clarify whether repeated exponents count all six permutations or distinct monomials.

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.