Prove2Me

lean_workbook_plus_9645

Proved

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

Let a,b,c ∈R\in R such that ac+bd=0. Prove that a+b+c+d2≤a2+b2+c2+d22\frac{a+b+c+d}{2} \le \sqrt{\frac{a^2+b^2+c^2+d^2}{2}}

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_9645 (a b c d : ℝ) (h : a * c + b * d = 0) :
  (a + b + c + d) / 2 ≤ Real.sqrt ((a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) / 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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