lean_workbook_plus_39695

Proved

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

Illustrate the use of Cauchy-Schwarz's extended version for $p, q, x, y > 0$ : $\frac{x^2}{p} + \frac{y^2}{q} \geq \frac{(x+y)^2}{p+q}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_39695 (p q x y : ℝ) (hp : 0 < p) (hq : 0 < q) (hx : 0 < x) (hy : 0 < y) : (x ^ 2 / p + y ^ 2 / q) ≥ (x + y) ^ 2 / (p + q)   :=  by sorry

Source

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

View graph