lean_workbook_plus_81978

Proved

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

Prove that for $a, b, c, d > 0$ , \n $\frac{(a-b)^2}{a+b}+\frac{(c-d)^2}{c+d}\ge\frac{(a+c-b-d)^2}{a+b+c+d}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_81978 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a - b) ^ 2 / (a + b) + (c - d) ^ 2 / (c + d) ≥ (a + c - b - d) ^ 2 / (a + b + c + d)   :=  by sorry

Source

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

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