lean_workbook_plus_2131

Proved

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

prove: $a^{2}b^{2}+b^{2}c^{2}+c^{2}a^{2}\leq\frac{(a^{2}+b^{2}+c^{2})^{2}}{3}$ where $a,b,c > 0$ using the Cauchy-Schwarz inequality

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2131 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 * b^2 + b^2 * c^2 + c^2 * a^2 ≤ (a^2 + b^2 + c^2)^2 / 3   :=  by sorry

Source

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

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