lean_workbook_plus_67503

Proved

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

By AM-HM: $\frac{a+b}{2} \geq \frac{2}{\frac{1}{a}+\frac{1}{b}} \implies a+b \geq \frac{4}{\frac{1}{a}+\frac{1}{b}} = \frac{1}{\frac{1}{4a}+\frac{1}{4b}} \implies \frac{1}{4a}+\frac{1}{4b} \geq \frac{1}{a+b}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_67503  (a b : ℝ)
  (h₀ : 0 < a ∧ 0 < b) :
  1 / (4 * a) + 1 / (4 * b) ≥ 1 / (a + b)   :=  by sorry

Source

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

View graph