lean_workbook_plus_78362

Proved

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

By AM-GM, prove that $3x^4+y^4 \geq 4x^3y$ , $3y^4+z^4 \geq 4y^3z$ , and $3z^4+x^4 \geq 4z^3x$ for real numbers $x$ , $y$ , and $z$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78362 (x y z : ℝ) : 3 * x ^ 4 + y ^ 4 ≥ 4 * x ^ 3 * y ∧ 3 * y ^ 4 + z ^ 4 ≥ 4 * y ^ 3 * z ∧ 3 * z ^ 4 + x ^ 4 ≥ 4 * z ^ 3 * x   :=  by sorry

Source

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

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