lean_workbook_plus_70775

Proved

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

(If $a,b,c,d\in\mathbb{R}^+$ and $a+b+c+d=1$ , prove that $ab+bc+cd\le\frac{1}{4}$ .)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_70775 (a b c d : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hd : d > 0) (hab : a + b + c + d = 1) : a * b + b * c + c * d ≤ 1 / 4   :=  by sorry

Source

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

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