A cyclic fifth-degree inequality on nonnegative variables

Proved

WorkbookSource.base_6095

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

lean-workbooksource-checked

Let $a$ , $b$ and $c$ be non-negative numbers. Prove that: $a^4b+b^4c+c^4a\geq abc(a^2+b^2+c^2)$

Source: InternLM Lean-Workbook, record lean_workbook_6095 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6095 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : a^4 * b + b^4 * c + c^4 * a ≥ a * b * c * (a^2 + b^2 + c^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6095; Apache-2.0

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