lean_workbook_plus_51582

Proved

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

it is just AM-GM \n $a^4 + a^4 + a^4 + b^4 \geq 4\sqrt[4]{a^{12}b^4} = 4a^3b$ \n $b^4 + b^4 + b^4 + c^4 \geq 4\sqrt[4]{b^{12}c^4} = 4b^3c$ \n $c^4 + c^4 + c^4 + a^4 \geq 4\sqrt[4]{c^{12}a^4} = 4c^3a$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_51582  (a b c : ℝ) :
  a^4 + a^4 + a^4 + b^4 ≥ 4 * (a^3 * b) ∧
  b^4 + b^4 + b^4 + c^4 ≥ 4 * (b^3 * c) ∧
  c^4 + c^4 + c^4 + a^4 ≥ 4 * (c^3 * a)   :=  by sorry

Source

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

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