lean_workbook_plus_12666

⚠️ 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.

Prove that there do not exist distinct reals $x,y,u,v$ such that $x^2+y^2=u^2+v^2 , x^3+y^3=u^3+v^3$ simultaneously hold.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_12666 (x y u v : ℝ) (h₁ : x ≠ u ∨ x ≠ v) (h₂ : y ≠ u ∨ y ≠ v) (h₃ : x ≠ y) (h₄ : u ≠ v) (hx : x^2 + y^2 = u^2 + v^2) (hy : x^3 + y^3 = u^3 + v^3) : False   :=  by sorry

The formal disproof uses a repeated pair, while the stronger source counterexample is independently documented in workbook9479.

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

Proposed corrected statement

Replace the OR distinctness clauses by genuine pairwise distinctness, but then answer the source nonexistence claim negatively: four distinct real numbers with both moments equal do exist.

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.