Prove2Me

lean_workbook_plus_15029

Proved

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

By Trivial Inequality, (a−b)2+(b−c)2+(c−a)2≥0  ⟹  a2+b2+c2≥ab+bc+ca(a-b)^2+(b-c)^2+(c-a)^2 \geq 0 \implies a^2+b^2+c^2 \geq ab+bc+ca , with equality when a=b=ca=b=c . (So basically your question is to find the equality case of the inequality a2+b2+c2≥ab+bc+caa^2+b^2+c^2 \geq ab+bc+ca .)

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_15029 (a b c : ℝ) : (a - b) ^ 2 + (b - c) ^ 2 + (c - a) ^ 2 ≥ 0 → a ^ 2 + b ^ 2 + c ^ 2 ≥ a * b + b * c + c * a   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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