lean_workbook_plus_19538

⚠️ 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: $0\leq {\frac { \left( y-1 \right) \left( z-x \right) }{ \left( z+xy \right) \left( y+xz \right) }}+{\frac { \left( z-1 \right) \left( x-y \right) }{ \left( x+yz \right) \left( z+xy \right) }}+{\frac { \left( x-1 \right) \left( y-z \right) }{ \left( y+xz \right) \left( x+yz \right) }}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_19538 : ∀ x y z : ℝ, (x - 1) * (y - z) / (y + x * z) * (x + y * z) + (y - 1) * (z - x) / (z + x * y) * (x + z * y) + (z - 1) * (x - y) / (x + y * z) * (y + z * x) ≥ 0   :=  by sorry

The target parses division followed by multiplication and changes factors; even the corrected rational sum is not nonnegative for every positive triple.

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 every full product denominator exactly as in the source, and recover the source ordering or relation on x,y,z.

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.