lean_workbook_plus_64489

Proved

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

If $a, b,c,d > 0$ and $a^2+b^2 \ge c^2+d^2$ . Prove that : \n

\frac{b}{a+c}+\frac{a}{b+d} \geq 1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64489 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (hab: a^2+b^2 >= c^2+d^2) : b / (a + c) + a / (b + d) ≥ 1   :=  by sorry

Source

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

View graph