lean_workbook_plus_42088

Proved

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

Let $a,b,c\geq0$ .Prove that: \n $a^3 + b^3 + c^3 - 3abc\geq2(\dfrac{b + c}{2} - a)^3$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_42088 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : a^3 + b^3 + c^3 - 3*a*b*c ≥ 2 * ((b + c) / 2 - a)^3   :=  by sorry

Source

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

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