lean_workbook_plus_45947

Proved

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

Show that $\frac{a}{a+3b}+\frac{b}{b+3c}+\frac{c}{c+3d}+\frac{d}{d+3a}<3$ for positive real numbers $a, b, c, d$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_45947 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : a / (a + 3 * b) + b / (b + 3 * c) + c / (c + 3 * d) + d / (d + 3 * a) < 3   :=  by sorry

Source

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

View graph