A cyclic ratio sum with a normalized cubic correction

Proved

WorkbookSource.base_6317

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

lean-workbooksource-checked

If $a, b, c>0$ prove that $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}+\frac{9(a^3+b^3+c^3)}{(a+b+c)^3}\ge\frac{5}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_6317 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6317 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (a + b) + b / (b + c) + c / (c + a) + (9 * (a ^ 3 + b ^ 3 + c ^ 3)) / (a + b + c) ^ 3) ≥ 5 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6317; Apache-2.0

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