lean_workbook_plus_42117

Proved

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

Let $a,b,c$ be reals such that $b-c \geq a-b \geq 0$ . Show that \n $3(a^2b+b^2a+b^2c+c^2b+a^2c+c^2a) \geq 2(a^3+b^3+c^3)+12abc$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_42117 (a b c : ℝ) (h : b - c ≥ a - b ∧ a - b ≥ 0) :
  3 * (a^2 * b + b^2 * a + b^2 * c + c^2 * b + a^2 * c + c^2 * a) ≥
    2 * (a^3 + b^3 + c^3) + 12 * a * b * c   :=  by sorry

Source

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

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