lean_workbook_plus_50021

Proved

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

Let a,b,c,d>0 such that $ac+bd=2.$ Prove that $(ad-bc)^2 + 2\ge ad+bc$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_50021 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (hab : a * c + b * d = 2) : (a * d - b * c) ^ 2 + 2 ≥ a * d + b * c   :=  by sorry

Source

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

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