lean_workbook_plus_31842

Proved

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

Let $a,$ $b,$ $c$ be positive real numbers. Prove that $\frac {a}{b} + \frac {b}{c} + \frac {c}{a} \ge \frac {a + b}{b + c} + \frac {b + c}{a + b} + 1.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31842 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : a / b + b / c + c / a >= (a + b) / (b + c) + (b + c) / (a + b) + 1   :=  by sorry

Source

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

View graph