lean_workbook_plus_65330

Proved

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

Let a,b,c,d be four positive real numbers. Prove that $(a - b)(b - c)(c - d)(d - a) + (a - c)^{2}(b - d)^{2}\geq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_65330 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) :  (a - b) * (b - c) * (c - d) * (d - a) + (a - c) ^ 2 * (b - d) ^ 2 ≥ 0   :=  by sorry

Source

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

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