lean_workbook_plus_3103

⚠️ 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.

Solve the system of inequations on $\mathbb{R}^2$ \n\n $\left\{ \begin{array}{l} \left( {x^2 + y^2 - 1} \right)^2 + x + y \le \left( {x^2 + y^2 } \right)\left( {x + y - 1} \right) + 1 \ 2x + 4y - \sqrt {10} - 3 \ge 0 \ \end{array} \right.$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_3103 : { (x, y) : ℝ × ℝ | (x^2 + y^2 - 1)^2 + x + y ≤ (x^2 + y^2) * (x + y - 1) + 1 ∧ 2 * x + 4 * y - Real.sqrt 10 - 3 ≥ 0} = {(x, y) : ℝ × ℝ | (x^2 + y^2 - 1)^2 + x + y ≤ (x^2 + y^2) * (x + y - 1) + 1 ∧ (2 * x + 4 * y - Real.sqrt 10 - 3 >= 0 ∨ 2 * x + 4 * y - Real.sqrt 10 - 3 <= 0)}   :=  by sorry

The proposed solution set replaces a required half-plane by a tautological sign disjunction, adding(0,0).

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

Proposed corrected statement

Restore the original find-all/evaluation task without the inserted answer; prove the resulting characterization in both directions. No replacement fixed answer is asserted here. Original task: Solve the system of inequations on $\mathbb{R}^2$ \n\n $\left\{ \begin{array}{l} \left( {x^2 + y^2 - 1} \right)^2 + x + y \le \left( {x^2 + y^2 } \right)\left( {x + y - 1} \right) + 1 \ 2x + 4y - \sqrt {10} - 3 \ge 0 \ \end{array} \right.$

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.