lean_workbook_plus_64225

Disproved

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

Prove the inequality\n\n $\frac{1}{2+b^2+c^2}+\frac{1}{2+c^2+a^2}+\frac{1}{2+a^2+b^2}\leq\frac{3}{4}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64225 : ∀ a b c : ℝ, (1 / (2 + b ^ 2 + c ^ 2) + 1 / (2 + c ^ 2 + a ^ 2) + 1 / (2 + a ^ 2 + b ^ 2) : ℝ) ≤ 3 / 4   :=  by sorry

Source

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

View graph