lean_workbook_plus_49436

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

We wish to solve $x^3-x-7=0$ . Note that this is already in the form of a depressed cubic. Let $u+v =x$ . This gives us $u^3+v^3+(3uv-1)(u+v)-7=0$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_49436 (x : ℝ) (hx : x^3 - x - 7 = 0) : ∃ u v : ℝ, u + v = x ∧ u^3 + v^3 + (3 * u * v - 1) * (u + v) - 7 = 0   :=  by sorry

Solving the cubic is replaced by rewriting an already assumed root with two unrestricted summands.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Give explicit real root(s) of x³−x−7=0 and prove the characterization; in a Cardano reduction require the substantive auxiliary relations 3uv=1 and u³+v³=7, not just u+v=x.

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.