lean_workbook_plus_81628

⚠️ 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_81628 (x y u v : ℝ) (h₁ : x ≠ u) (h₂ : x ≠ v) (h₃ : y ≠ u) (h₄ : y ≠ v) (h₅ : x^2 + y^2 = u^2 + v^2) (h₆ : x^3 + y^3 = u^3 + v^3) : False   :=  by sorry

Four cross inequalities do not encode four pairwise distinct reals; the accepted counterexample uses x=y.

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

Proposed corrected statement

Require all six pairwise inequalities among x,y,u,v if that is the intended “distinct reals” meaning, and re-evaluate the no-solution claim on that domain. The present counterexample does not validate or refute the strengthened assertion.

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.