A cyclic cubic reciprocal sum bounds a normalized cubic sum

Proved

WorkbookSource.base_7145

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

lean-workbooksource-checked

Given $a;b;c>0$ , without using SOS method, prove that: $\frac{a^3}{b+c}+\frac{b^3}{c+a}+\frac{c^3}{a+b} \geq \frac{3}{2}.\frac{a^3+b^3+c^3}{a+b+c}$

Source: InternLM Lean-Workbook, record lean_workbook_7145 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7145 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 / (b + c) + b^3 / (c + a) + c^3 / (a + b)) ≥ 3/2 * (a^3 + b^3 + c^3) / (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7145; Apache-2.0

View graph