lean_workbook_plus_56537

Disproved

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

For $a,b>0,\frac{1}{a}+\frac{1}{b}=1,$ prove that $\frac{1}{a^2+4}+\frac{1}{b^2+4}\ge\frac{1}{2} .$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_56537 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : 1 / a + 1 / b = 1) : 1 / (a ^ 2 + 4) + 1 / (b ^ 2 + 4) ≥ 1 / 2   :=  by sorry

Source

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

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