Prove2Me

lean_workbook_plus_19594

Proved

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

We have this by Cauchy Schwarz: 2(a2+b2)(b2+c2)(c2+a2)=[(a−b)2+(a+b)2][c2(a−b)2+(c2+ab)2]≥[c(a−b)2+(c2+ab)(a+b)]2=[(a+b)(b+c)(c+a)−4abc]22(a^2+b^2)(b^2+c^2)(c^2+a^2)=[(a-b)^2+(a+b)^2][c^2(a-b)^2+(c^2+ab)^2] \geq [c(a-b)^2+(c^2+ab)(a+b)]^2=[(a+b)(b+c)(c+a)-4abc]^2

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_19594 : ∀ a b c : ℝ, 2 * (a ^ 2 + b ^ 2) * (b ^ 2 + c ^ 2) * (c ^ 2 + a ^ 2) ≥ ((a + b) * (b + c) * (c + a) - 4 * a * b * c) ^ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

View graph