lean_workbook_plus_40424

Proved

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

Show that for all positive real numbers $a,b,c$ and $d$ , $\frac{a^2}{a^2+bc}+ \frac{b^2}{b^2+cd}+\frac{c^2}{c^2+da}+\frac{d^2}{d^2+ab} \leq 3$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40424 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a^2 / (a^2 + b * c) + b^2 / (b^2 + c * d) + c^2 / (c^2 + d * a) + d^2 / (d^2 + a * b) ≤ 3)   :=  by sorry

Source

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

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