lean_workbook_plus_40026

Proved

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

Let $a,b,c,d \in \mathbb{R}_{+}$ and $a+b +c +d =1$ , show that $ab +bc +cd \leq \dfrac{1}{4}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40026 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (habc : a + b + c + d = 1) : a * b + b * c + c * d ≤ 1 / 4   :=  by sorry

Source

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

View graph