A translated quartic inequality

Proved

WorkbookSource.problem_28159

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

lean-workbooksource-checked

There is a number: a = m - 1 a\in R^ + So we must prove: $16(a + 1)^2 + 16\leq(a + 1)^4 + 32(a + 1)$ $16a^2 + 32a + 32\leq(a + 1)^4 + 32a + 32$ $16a^2\leq(a + 1)^4$ $4a\leq(a + 1)^2$ $0\leq(a - 1)^2$

Source: InternLM Lean-Workbook, record lean_workbook_28159 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_28159  (a : ℝ)
  (h₀ : 0 < a) :
  16 * (a + 1)^2 + 16 ≤ (a + 1)^4 + 32 * (a + 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28159; Apache-2.0

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