Prove2Me

lean_workbook_plus_15729

Proved

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

Prove: 3(x2+y2+z2)≥(x+y+z)2≥3(xy+yz+zx)3(x^2 + y^2 + z^2)\geq (x + y + z)^2\geq 3(xy + yz + zx)

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_15729 (x y z : ℝ) : 3 * (x ^ 2 + y ^ 2 + z ^ 2) ≥ (x + y + z) ^ 2 ∧ (x + y + z) ^ 2 ≥ 3 * (x * y + y * z + z * x)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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