lean_workbook_plus_325

⚠️ 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 that for non-negative numbers $a, b, c, d, e, f$, the following identity holds: $3/2(ad-bc)^2 + 3/2(be-cd)^2 + 3/2(ac-de)^2 + (a-b)^2ab + (b-c)^2bc + (c-d)^2cd + (d-e)^2de + (e-a)^2ea + 5/2(ab+bc+cd+de+ea-ac-bd-ec-ad-be)^2 + (e-b)^2be + (d-a)^2ad + (c-e)^2ec + (b-d)^2bd + (a-c)^2ac + 3/2(bd-ea)^2 + 3/2(ec-ab)^2$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_325 : ∀ a b c d e f : ℝ, a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0 ∧ d ≥ 0 ∧ e ≥ 0 ∧ f ≥ 0 → 3 / 2 * (a * d - b * c) ^ 2 + 3 / 2 * (b * e - c * d) ^ 2 + 3 / 2 * (a * c - d * e) ^ 2 + (a - b) ^ 2 * a * b + (b - c) ^ 2 * b * c + (c - d) ^ 2 * c * d + (d - e) ^ 2 * d * e + (e - a) ^ 2 * e * a + 5 / 2 * (a * b + b * c + c * d + d * e + e * a - a * c - b * d - e * c - a * d - b * e) ^ 2 + (e - b) ^ 2 * b * e + (d - a) ^ 2 * a * d + (c - e) ^ 2 * e * c + (b - d) ^ 2 * b * d + (a - c) ^ 2 * a * c + 3 / 2 * (b * d - e * a) ^ 2 + 3 / 2 * (e * c - a * b) ^ 2 = 0   :=  by sorry

The source supplies only a sum-of-squares expression with no second side; the target invents equality to zero.

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

Proposed corrected statement

Recover the missing other side of the intended identity. The displayed expression is nonnegative for nonnegative variables, but zero is not generally its value.

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.