lean_workbook_plus_11871

Proved

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

Given $abc=0$ , prove the inequality $\sum_{cyc}a^2b^4 + \sum_{cyc}a^3bc^2 \geq 2 \sum_{cyc}a^3b^2c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11871 (a b c : ℝ) (h : a * b * c = 0) :
  a ^ 2 * b ^ 4 + b ^ 2 * c ^ 4 + c ^ 2 * a ^ 4 + a ^ 3 * b * c ^ 2 + b ^ 3 * c * a ^ 2 + c ^ 3 * a * b ^ 2 ≥
  2 * (a ^ 3 * b ^ 2 * c + b ^ 3 * c ^ 2 * a + c ^ 3 * a ^ 2 * b)   :=  by sorry

Source

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

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