A rational bound from a square

Proved

WorkbookSource.problem_47872

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

lean-workbooksource-checked

$a^4+1\ge 2a^2 \implies \dfrac{a^3}{a^4+1}\le \frac{a}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_47872 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_47872 (a : ℝ) (ha : a ≥ 0) : a^3 / (a^4 + 1) ≤ a / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_47872; Apache-2.0

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