lean_workbook_plus_67558

Proved

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

Let $a$ and $b$ be two positive real numbers with $a \le 2b \le 4a$ . Prove that $4ab \le2 (a^2+ b^2) \le 5 ab$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_67558 (a b : ℝ) (h1 : 0 < a ∧ 0 < b) (h2 : a ≤ 2 * b) (h3 : 2 * b ≤ 4 * a) :
  4 * a * b ≤ 2 * (a ^ 2 + b ^ 2) ∧ 2 * (a ^ 2 + b ^ 2) ≤ 5 * a * b   :=  by sorry

Source

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

View graph