lean_workbook_plus_384

Proved

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

Prove that for positive real numbers $a, b, c$ :\n

2(a^4+b^4+c^4)+4(a^2b^2+c^2a^2+b^2c^2) \ge 3(a^3c+b^3a+c^3b)+3abc(a+b+c)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_384 {a b c : ℝ} (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 2 * (a ^ 4 + b ^ 4 + c ^ 4) + 4 * (a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2) ≥ 3 * (a ^ 3 * c + b ^ 3 * a + c ^ 3 * b) + 3 * a * b * c * (a + b + c)   :=  by sorry

Source

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

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