lean_workbook_plus_32025

Proved

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

By Rearrangement Inequality we have $a^4+b^4+c^4 \geqslant |b^3c| + |c^3a| + |a^3b| \geqslant -b^3c -c^3a -a^3b$ , so $ab^3+bc^3+ca^3 = \sum_{cyc} (-b-c)b^3 \leqslant 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32025  (a b c : ℝ)
  (h₀ : 0 ≤ a ∧ 0 ≤ b ∧ 0 ≤ c)
  (h₁ : a + b + c = 0) :
  a * b^3 + b * c^3 + c * a^3 ≤ 0   :=  by sorry

Source

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

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