lean_workbook_plus_69392

Proved

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

we have: $\frac{1}{\frac{1}{a^2}}+\frac{1}{\frac{1}{b^2}}+\frac{1}{\frac{1}{c^2}} \geq \frac{9}{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}$ \nhence, $\frac{1}{9} \left(a^2+b^2+c^2 \right) \geq \frac{1}{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_69392  (a b c : ℝ)
  (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) :
  1 / 9 * (a^2 + b^2 + c^2) ≥ 1 / (1 / a^2 + 1 / b^2 + 1 / c^2)   :=  by sorry

Source

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

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