lean_workbook_plus_12013

⚠️ 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.

note that : $t=x+1/x$ then $x^{5}+\frac{1}{x^{5}}-1=(t-1)((t-1)(t^{3}+2t^{2}-2t-6)+5)$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_12013 : ∀ x : ℝ, x^5 + 1/(x^5) - 1 = (x + 1/x - 1)*((x + 1/x - 1)*(x^3 + 2*x^2 - 2*x - 6) + 5)   :=  by sorry

The target substitutes x for t inside the cubic; the source’s plus5 is also wrong, as seen at x=1.

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

Proposed corrected statement

Use t=x+1/x consistently, require x≠0, and correct the source factorization to(t−1)((t−1)(t³+2t²−2t−6)−5).

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.