A quotient bound involving a square root

Proved

WorkbookSource.problem_30934

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

For the second note that: $\frac{\sqrt{1-x^2}}{1+x^2}\leq\frac{1}{1+x^2}$ .

Source: InternLM Lean-Workbook, record lean_workbook_30934 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_30934 : ∀ x, Real.sqrt (1 - x ^ 2) / (1 + x ^ 2) ≤ 1 / (1 + x ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30934; Apache-2.0

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