lean_workbook_plus_52916

Proved

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

If $a$ , $b$ and $c$ are positive real numbers, not all equal, prove that $6abc<a^2(b+c)+b^2(c+a)+c^2(a+b)<2\left(a^3+b^3+c^3\right)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_52916 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a ≠ b) (hbc : b ≠ c) (hca : a ≠ c) : 6 * a * b * c < a ^ 2 * (b + c) + b ^ 2 * (c + a) + c ^ 2 * (a + b) ∧ a ^ 2 * (b + c) + b ^ 2 * (c + a) + c ^ 2 * (a + b) < 2 * (a ^ 3 + b ^ 3 + c ^ 3)   :=  by sorry

Source

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

View graph