lean_workbook_plus_15426

Proved

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

Let $a \ge b \ge c \0$ and $a+c \ge 2b$ , $a \le 2c$ . Prove that : $2\left(\sum{a}\right)^3 + 27abc \ge 9(ab+bc+ca)(a+b+c)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15426 (a b c : ℝ) (h1 : a ≥ b ∧ b ≥ c ∧ c ≥ 0) (h2 : a + c ≥ 2 * b) (h3 : a ≤ 2 * c) : 2 * (a + b + c) ^ 3 + 27 * a * b * c ≥ 9 * (a * b + b * c + c * a) * (a + b + c)   :=  by sorry

Source

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

View graph