lean_workbook_plus_6222

Proved

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

Let $a$ , $b$ , and $c$ be non-negative reals. Prove that $a^3+b^3+c^3+6abc\ge \frac{(a+b+c)^3}{4}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6222 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : a^3 + b^3 + c^3 + 6 * a * b * c ≥ (a + b + c)^3 / 4   :=  by sorry

Source

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

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