lean_workbook_plus_48642

Disproved

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

We have $\frac{x^{2}+y^{2}+2}{(x^{2}+1)(y^{2}+1)}\geq\frac{10xy+7}{(xy+1)(2xy+5)}$ , and just denote $xy=t$ , and we have $xy\le \frac{1}{2}$ , and we get this $3(2t+5)(t+1)\geq(t^{2}+2)(10t+7)\Leftrightarrow$ $(2t-1)(5t^2+2t+1)\le 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_48642 : ∀ x y : ℝ, (x^2 + y^2 + 2) / (x^2 + 1) / (y^2 + 1) ≥ (10 * x * y + 7) / (x * y + 1) / (2 * x * y + 5)   :=  by sorry

Source

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

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