lean_workbook_plus_43757

Proved

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

Prove that $(a+b)(\frac{1}{b+d}+\frac{1}{a+c}) \ge \frac{4(a+b)}{a+b+c+d}$ given $a,b,c,d>0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_43757 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a + b) * (1 / (b + d) + 1 / (a + c)) ≥ 4 * (a + b) / (a + b + c + d)   :=  by sorry

Source

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

View graph