A cyclic fifth-power ratio bounds a fourth power of the total

Proved

WorkbookSource.base_50076

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

lean-workbooksource-checked

Prove that $\frac{a^5}{b}+\frac{b^5}{c}+\frac{c^5}{a}\geq\frac{1}{27} \cdot (a+b+c)^4$ for all $a,b,c >0$

Source: InternLM Lean-Workbook, record lean_workbook_50076 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_50076 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^5 / b + b^5 / c + c^5 / a) ≥ 1 / 27 * (a + b + c)^4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_50076; Apache-2.0

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