lean_workbook_plus_6915

Proved

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

Let $a$ , $b$ , $c$ be positive real numbers . Prove that ${{a+b}\over{a+2b}} + {{b+c}\over{b+2c}} + {{c+a}\over{c+2a}}<\frac{5}{2}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6915 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → (a + b) / (a + 2 * b) + (b + c) / (b + 2 * c) + (c + a) / (c + 2 * a) < 5 / 2   :=  by sorry

Source

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

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