lean_workbook_plus_7687

⚠️ 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 $a,b,c$ are positve real numbers. Prove that $\left( \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \right) \ge \frac{3}{2} \left( \frac{a+c}{b}+ \frac{a+b}{c}+\frac{b+c}{a} \right)$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_7687 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a) ≥ 3 / 2 * (a + c) / b + (a + b) / c + (b + c) / a   :=  by sorry

The multiplier 3/2 applies only to the first formal summand. Even the fully parenthesized source is false at a=b=c=1 (3≥9).

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

Proposed corrected statement

Recover the intended coefficients/direction from the source; both the transcription and the claimed inequality need correction. Do not treat parentheses alone as a repair.

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.