lean_workbook_plus_52651

Proved

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

Arithmetic Mean - Quadratic Mean (or Root-Mean Square, you might know it as that) $\frac{a+b+c}{3} \le \sqrt{\frac{a^2+b^2+c^2}{3}}$ exactly as used above.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_52651 (a b c : ℝ) : (a + b + c) / 3 ≤ Real.sqrt ((a ^ 2 + b ^ 2 + c ^ 2) / 3)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph