Prove2Me

lean_workbook_plus_14178

Proved

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

Prove the following chain inequality for all non-negative real numbers a,ba,b and cc: 3(a2+b2+c2)≥(a+b+c)2≥3(ab+bc+ca)3(a^2 + b^2 + c^2) \ge (a+b+c)^2 \ge 3(ab+bc+ca).

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_14178 (a b c: ℝ) : 3 * (a ^ 2 + b ^ 2 + c ^ 2) ≥ (a + b + c) ^ 2 ∧ (a + b + c) ^ 2 ≥ 3 * (a * b + b * c + c * a)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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