lean_workbook_plus_20784

⚠️ 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.

If $x+y=z,xy=t$ we get $2(z^{5}+1)=5t(2z^{3}-2zt+z^{2}-2t+1).$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_20784 : ∀ x y z t : ℂ, x + y = z ∧ x * y = t → 2 * (z^5 + 1) = 5 * t * (2 * z^3 - 2 * z * t + z^2 - 2 * t + 1)   :=  by sorry

The source substitution comes from an omitted original equation, but the target assumes only sum/product definitions.

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 that original equation and prove its equivalence to the displayed relation after z=x+y,t=xy.

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.