A fourth power difference inequality

Proved

WorkbookSource.problem_23578

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Given $a, b, c$ are real numbers. Prove that: $(a - b)^4 + (b - c)^4 + (c - a)^4 \geq\ 8(a - b)^2(c - a)(c - b)$

Source: InternLM Lean-Workbook, record lean_workbook_23578 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_23578 (a b c : ℝ) : (a - b) ^ 4 + (b - c) ^ 4 + (c - a) ^ 4 ≥ 8 * (a - b) ^ 2 * (c - a) * (c - b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23578; Apache-2.0

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