lean_workbook_plus_50078

Proved

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

Prove that for positive real numbers $a, b, c$ with $a \geq b \geq c$ and $abc = 1$ , the inequality $\frac{a}{b+a} + \frac{c}{a+c} + \frac{b}{b+c} \leq 2$ holds.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_50078 (a b c : ℝ) (h1 : a ≥ b ∧ b ≥ c) (h2 : 0 < a ∧ 0 < b ∧ 0 < c) (h3 : a * b * c = 1) : a / (b + a) + c / (a + c) + b / (b + c) ≤ 2   :=  by sorry

Source

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

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