lean_workbook_plus_23179

Proved

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

Prove inequality, with $a$ and $b$ nonnegative real numbers: $\frac{a+b}{1+a+b}\leq \frac{a}{1+a} + \frac{b}{1+b} \leq \frac{2(a+b)}{2+a+b}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_23179 (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) : (a + b) / (1 + a + b) ≤ a / (1 + a) + b / (1 + b) ∧ a / (1 + a) + b / (1 + b) ≤ (2 * (a + b)) / (2 + a + b)   :=  by sorry

Source

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

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