lean_workbook_plus_27487

Proved

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

Let $x,y,z,t$ be positive real numbers. Prove that $xy+yz+zt+tx \leq \frac{1}{4} (x+y+z+t)^2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27487 (x y z t : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (ht : t > 0) : x * y + y * z + z * t + t * x ≤ 1 / 4 * (x + y + z + t) ^ 2   :=  by sorry

Source

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

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