lean_workbook_plus_30415

Proved

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

prove $\frac{a^3+b^3+c^3}{3}\geq abc+\frac{3}{4}|(a-b)(b-c)(c-a)|$ given $a,b,c>0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_30415 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a^3 + b^3 + c^3) / 3 ≥ a * b * c + (3 / 4) * |(a - b) * (b - c) * (c - a)|   :=  by sorry

Source

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

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