lean_workbook_plus_18127

⚠️ 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.

$x^2+y^2+(x+y)^2=2$ - has solution $(x,y)=(1,0),(-1,0),(0,1),(0,-1),(1,-1)$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_18127 : { (x,y) : ℝ × ℝ | x^2 + y^2 + (x + y)^2 = 2} =  { (1,0), (-1,0), (0,1), (0,-1), (1,-1)}   :=  by sorry

The source says “has solution”, while the formalization invents an exhaustive finite real solution set.

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

Proposed corrected statement

State that each of the five listed pairs solves the equation, as the prose says; do not claim that these exhaust the real solutions. If a complete integer classification was intended, specify ℤ and recover the missing point(-1,1).

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.