lean_workbook_plus_14861

Proved

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

Prove that for $a, b, c, d > 0$ , \n $(a+b+c+d)(abc+bcd+cda+dab)\le (a+b)(a+c)(b+d)(c+d)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14861 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a + b + c + d) * (a * b * c + b * c * d + c * d * a + d * a * b) ≤ (a + b) * (a + c) * (b + d) * (c + d)   :=  by sorry

Source

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

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