lean_workbook_plus_71830

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that for positive real numbers $a, b, c$ , the following inequality holds: $ab^3+ac^3+bc^3+ba^3+ca^3+cb^3 \le 2(a^4+b^4+c^4)$ using the rearrangement inequality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_71830 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a * b ^ 3 + a * c ^ 3 + b * c ^ 3 + b * a ^ 3 + c * a ^ 3 + c * b ^ 3 ≤ 2 * (a ^ 4 + b ^ 4 + c ^ 4)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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