lean_workbook_plus_65805

Proved

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

Prove that: $\left(a+b+c \right)^2 \left[\sum \left(a-b \right)^2 \right] \geqslant 2 \left[\sum \left(a-b \right)^2\left(a+c \right) \left(b+c \right) \right]$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_65805 {a b c : ℝ} :
  (a + b + c) ^ 2 * ((a - b) ^ 2 + (b - c) ^ 2 + (c - a) ^ 2) ≥
    2 * ((a - b) ^ 2 * (a + c) * (b + c) + (b - c) ^ 2 * (b + a) * (c + a) + (c - a) ^ 2 * (c + b) * (a + b))   :=  by sorry

Source

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

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