lean_workbook_plus_17634

⚠️ 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.

$<-> 4(x+y+z)^6 \ge 27(x+y+z).(x^2+y^2+z^2+xy+yz+zx)^2$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_17634 : ∀ x y z : ℝ, (x + y + z) ^ 6 ≥ 27 * (x + y + z) * (x ^ 2 + y ^ 2 + z ^ 2 + x * y + y * z + z * x) ^ 2   :=  by sorry

The leading coefficient4 in the source was dropped; the excerpt also gives no normalization and mixed degrees preclude a general positive-domain theorem.

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

Proposed corrected statement

Restore4(x+y+z)^6 and recover the source normalization/preceding equivalence. Positive variables alone do not suffice under arbitrary scaling.

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.