lean_workbook_plus_71895

Proved

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

Let $a,b,c>0$ . Prove that $\dfrac{a+b+c}{1+a+b+c}\geq\dfrac{a}{1+3a}+\dfrac{b}{1+3b}+\dfrac{c}{1+3c}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_71895 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) / (1 + a + b + c) ≥ a / (1 + 3 * a) + b / (1 + 3 * b) + c / (1 + 3 * c)   :=  by sorry

Source

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

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