lean_workbook_plus_79596

Proved

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

proofwiki

prove that: $\sqrt[6]{\frac{(a+b)(b+c)(c+a)(a+d)(d+b)(d+c)}{64}} \geq \sqrt[3]{\frac{abc+bcd+cda+adb}{4}}$ , where $a;b;c;d>0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79596 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : ((a + b) * (b + c) * (c + a) * (a + d) * (d + b) * (d + c) / 64)^(1 / 6) ≥ (a * b * c + b * c * d + c * d * a + d * a * b / 4)^(1 / 3)   :=  by sorry

Source

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

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