A cubic-over-linear lower bound at fixed sum three

Proved

WorkbookSource.base_15222

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

lean-workbooksource-checked

prove the inequality :

\sum_{cyc} \frac{a^3}{b+c} \ge \frac{3}{2}

Given $a, b, c$ are positive real numbers such that $a+b+c = 3$

Source: InternLM Lean-Workbook, record lean_workbook_15222 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15222 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : a^3 / (b + c) + b^3 / (a + c) + c^3 / (a + b) ≥ 3 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15222; Apache-2.0

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