lean_workbook_plus_1830

Proved

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

Let $a,b,c$ be positive real numbers . Prove that $\frac{a}{2a+b+c}+\frac{b}{a+2b+c}+\frac{c}{a+b+2c}\le\frac{3}{4} .$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1830 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → a / (2 * a + b + c) + b / (a + 2 * b + c) + c / (a + b + 2 * c) ≤ 3 / 4   :=  by sorry

Source

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

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