lean_workbook_plus_54512

⚠️ 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 $w$ is a non-real cube root of unity, show that $1+w+2^{2}= 0$ , and deduce that $(1+w)^{3}(1+2w+2w^{2})$ =1

Why this node was retired

The posted statement is

theorem lean_workbook_plus_54512 {w : ℂ} (hw : w ≠ 1) (hw2 : w^3 = 1) : 1 + w + w^2 = 0 ∧ (1 + w)^3 * (1 + w^2 + w) = 1   :=  by sorry

The second factor lost its two coefficients2; the source also has a visible w²/2² transcription typo.

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

Proposed corrected statement

For a nontrivial cube root of unity w, prove1+w+w²=0 and(1+w)³(1+2w+2w²)=1. State w≠1,w³=1.

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.