lean_workbook_plus_7810

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_7810 (a b c d : ℝ) (h1 : a > 0 ∧ b > 0 ∧ c > 0 ∧ d > 0 ∧ 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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