A cyclic fourth-power ratio with a difference product correction

Proved

WorkbookSource.plus_42465

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

lean-workbooksource-checked

If $a,b,c>0$ prove that

$\frac{a^4}{b}+\frac{b^4}{c}+\frac{c^4}{a}\geq a^3+b^3+c^3+2(a-b)(b-c)(c-a)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_42465 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_42465 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^4 / b + b^4 / c + c^4 / a ≥ a^3 + b^3 + c^3 + 2 * (a - b) * (b - c) * (c - a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_42465; Apache-2.0

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