lean_workbook_plus_55763

Proved

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

Prove that for all $a,b,c>0$ : \n $\frac{b+c}{a^2+bc}+\frac{a+c}{b^2+ac}+\frac{b+a}{c^2+ba} \le \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_55763 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (b + c) / (a ^ 2 + b * c) + (a + c) / (b ^ 2 + a * c) + (b + a) / (c ^ 2 + b * a) ≤ 1 / a + 1 / b + 1 / c   :=  by sorry

Source

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

View graph