A reciprocal quadratic sum with a product correction

Proved

WorkbookSource.base_23742

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

If $a,b$ are real numbers than prove that $\frac{a^2+1}{b^2+1}+\frac{b^2+1}{a^2+1}+\frac{3(a^2+1)(b^2+1)}{4}\geq2+a^2-ab+b^2$

Source: InternLM Lean-Workbook, record lean_workbook_23742 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_23742 (a b : ℝ) : (a^2 + 1) / (b^2 + 1) + (b^2 + 1) / (a^2 + 1) + (3 * (a^2 + 1) * (b^2 + 1)) / 4 ≥ 2 + a^2 - a * b + b^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23742; Apache-2.0

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