lean_workbook_plus_43343

Proved

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

Given positive reals a, b, c. Prove that: \n $\frac{a}{1+a(1+b)}+\frac{b}{1+b(1+c)}+\frac{c}{1+c(1+a)} \leq 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_43343 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a / (1 + a * (1 + b)) + b / (1 + b * (1 + c)) + c / (1 + c * (1 + a)) ≤ 1   :=  by sorry

Source

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

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