lean_workbook_plus_45111

Proved

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

Let $a,b,c$ be positive real numbers . \n $a^3+b^3+c^3-3abc\ge2 \left(\dfrac{b+c}{2}-a\right)^3.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_45111 (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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