lean_workbook_plus_76491

Proved

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

If $a,b,c >0$ and $a < b+c$ prove that : \n\n $\frac{a}{1+a} < \frac{b}{1+b}+\frac{c}{1+c}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76491 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a < b + c) : a / (1 + a) < b / (1 + b) + c / (1 + c)   :=  by sorry

Source

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

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