lean_workbook_plus_41586

Proved

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

Let $a,b,c,d > 0$ and $a^2b^2+b^2c^2+c^2d^2+d^2a^2\leq 2(b c+d a) .$ Prove that \n

ab-cd \leq1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41586 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (habcd : a * b * c * d = 1) (h : a^2 * b^2 + b^2 * c^2 + c^2 * d^2 + d^2 * a^2 ≤ 2 * (b * c + d * a)) : a * b - c * d ≤ 1   :=  by sorry

Source

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

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