lean_workbook_plus_38134

Proved

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

prove that $\frac{a}{1+a+ab}+\frac{b}{1+b+bc}+\frac{c}{1+c+ca}\leq 1$ given $a,b,c>0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_38134 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : a / (1 + a + a * b) + b / (1 + b + b * c) + c / (1 + c + c * a) ≤ 1   :=  by sorry

Source

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

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