A cyclic ratio sum with a normalized cubic correction

Proved

WorkbookSource.base_53041

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a, b, c>0$ . Prove that $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge\frac{7}{2}-\frac{3abc}{2(a^3+b^3+c^3)}$

Source: InternLM Lean-Workbook, record lean_workbook_53041 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_53041 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a) ≥ 7 / 2 - 3 * a * b * c / (2 * (a ^ 3 + b ^ 3 + c ^ 3))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_53041; Apache-2.0

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