Prove2Me

A one-variable reciprocal cubic inequality

Proved
WorkbookSource.base_9463

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

lean-workbooksource-checked

Use the AM-GM inequality to show that for all positive real numbers a and d such that d = 1, the following inequality holds: 1(a+1)3+1(a+1)3+18≥32(a+1)2\frac{1}{(a+1)^3}+\frac{1}{(a+1)^3}+\frac{1}{8}\ge\frac{3}{2(a+1)^2}

Source: InternLM Lean-Workbook, record lean_workbook_9463 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_9463 (a : ℝ) (ha : a > 0) : (1 / (a + 1) ^ 3 + 1 / (a + 1) ^ 3 + 1 / 8) ≥ 3 / (2 * (a + 1) ^ 2)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9463; Apache-2.0

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