lean_workbook_plus_21670

Proved

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

This is equivalent to:

4a^4+4b^4+4c^4\ge4a^2b^2+4b^2c^2+4c^2a^2,

a^4+b^4+c^4\ge a^2b^2+b^2c^2+c^2a^2,

which is true by AM-GM. ( $\frac{a^4}{2}+\frac{b^4}{2}\ge2\sqrt{\frac{a^4b^4}{4}}=a^2b^2.$ )

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21670 : ∀ a b c : ℝ, 4 * a ^ 4 + 4 * b ^ 4 + 4 * c ^ 4 ≥ 4 * a ^ 2 * b ^ 2 + 4 * b ^ 2 * c ^ 2 + 4 * c ^ 2 * a ^ 2   :=  by sorry

Source

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

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