lean_workbook_plus_28915

⚠️ 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.

Let $a,b,c$ be non-negative then prove $\frac{1}{(a+2b)^{2}}+\frac{1}{(b+2c)^{2}}+\frac{1}{(c+2a)^{2}}\ge \frac{1}{ab+bc+ca}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_28915 : ∀ a b c : ℝ, (a + 2 * b) ^ (-2:ℤ) + (b + 2 * c) ^ (-2:ℤ) + (c + 2 * a) ^ (-2:ℤ) ≥ (a * b + b * c + c * a) ^ (-1:ℤ)   :=  by sorry

Both the source domain and ordinary definedness of reciprocals need representation.

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 a,b,c≥0 and require the displayed denominators to be nonzero where ordinary reciprocals are used; do not permit a=b=0 with the totalized inverse interpretation.

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.