lean_workbook_plus_60772

⚠️ 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 $\dfrac{a}{b+c}+\dfrac{b}{a+c}-\dfrac{2(a+b)}{a+b+2c}=\dfrac{(a+b+c)(a-b)^2}{(b+c)(a+c)(a+b+2c)}\ge0$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_60772 : ∀ a b c : ℝ, (a / (b + c) + b / (a + c) - 2 * (a + b) / (a + b + 2 * c) : ℝ) = (a + b + c) * (a - b) ^ 2 / ((b + c) * (a + c) * (a + b + 2 * c)) ∧ (a / (b + c) + b / (a + c) - 2 * (a + b) / (a + b + 2 * c) : ℝ) ≥ 0   :=  by sorry

The rational identity and nonnegativity are asserted with zero/negative denominators.

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 a,b,c>0 and prove the exact identity and its nonnegative RHS; more generally state explicit sign and nonzero conditions on every factor.

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.