Prove2Me

lean_workbook_plus_76898

Proved

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

Prove that

(a−b)2+(b−c)2+(c−a)2≥∣(a−b)(b−c)∣+∣(b−c)(c−a)∣+∣(c−a)(a−b)∣(a-b)^2+(b-c)^2+(c-a)^2\geq|(a-b)(b-c)|+|(b-c)(c-a)|+|(c-a)(a-b)|
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_76898 (a b c : ℝ) : (a - b) ^ 2 + (b - c) ^ 2 + (c - a) ^ 2 ≥ |(a - b) * (b - c)| + |(b - c) * (c - a)| + |(c - a) * (a - b)|   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

View graph