lean_workbook_plus_72405

Proved

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

Let $a,b,c$ be positive real numbers. Prove that \n\n $\frac{a}{ab+a+1}+\frac{b}{bc+b+1}+\frac{c}{ca+c+1}\le1.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_72405 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a / (a * b + a + 1) + b / (b * c + b + 1) + c / (c * a + c + 1) ≤ 1   :=  by sorry

Source

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

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