lean_workbook_plus_1424

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_1424 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (habc : a * b * c > 0) (hcd : c * d * b > 0) (habd : a * b * d > 0) : (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

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