A weighted square inequality

Proved

WorkbookSource.problem_25201

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

prove that : $(px+qy)^2\leq px^2+qy^2$ for numbers $p,q > 0$ and $p+q < 1$

Source: InternLM Lean-Workbook, record lean_workbook_25201 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_25201 (x y : ℝ) (p q : ℝ) (hp : 0 < p) (hq : 0 < q) (hpq : p + q < 1) : (p * x + q * y) ^ 2 ≤ p * x ^ 2 + q * y ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_25201; Apache-2.0

View graph