lean_workbook_plus_44943

⚠️ 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.

The real numbers $a,b,c,x,y,z$ satisfy $a\geq b\geq c>0$ and $x\geq y\geq z>0$ . Prove that $\frac{a^{2}x^{2}}{(by+cz)(bz+cy)}+\frac{b^{2}y^{2}}{(cz+ax)(cx+az)}+\frac{c^{2}z^{2}}{(ax+by)(ay+bx)}$ is at least $\frac{3}{4}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_44943 :  ∀ a b c x y z : ℝ, a ≥ b ∧ b ≥ c ∧ c > 0 → x ≥ y ∧ y ≥ z ∧ z > 0 →    a^2 * x^2 / (b * y + c * z) * (b * z + c * y) + b^2 * y^2 / (c * z + a * x) * (c * x + a * z) + c^2 * z^2 / (a * x + b * y) * (a * y + b * x) ≥ 3 / 4   :=  by sorry

Put both factors inside each denominator: a²x²/((by+cz)(bz+cy)), and analogously for the other two terms.

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

Proposed corrected statement

Put both factors inside each denominator: a²x²/((by+cz)(bz+cy)), and analogously for the other two terms.

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.