Prove2Me

lean_workbook_plus_26209

Proved

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

There exists a simple proof after using the inequality:

2(a2+b2)(b2+c2)(c2+a2)≥(a+b)(b+c)(c+a)−4abc\sqrt{2(a^2+b^2)(b^2+c^2)(c^2+a^2)}\ge (a+b)(b+c)(c+a)-4abc
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_26209 (a b c : ℝ) :
  Real.sqrt (2 * (a ^ 2 + b ^ 2) * (b ^ 2 + c ^ 2) * (c ^ 2 + a ^ 2)) ≥
    (a + b) * (b + c) * (c + a) - 4 * a * b * c   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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