lean_workbook_plus_75540

Proved

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

In this case we need to prove that $16(a + 2)^4(2a + 1)\geq243(a + 1)^4,$ which is equivalent to \n\n $f(a)\geq0,$ where $f(a) = 4\ln(a + 2) + \ln(2a + 1) - 4\ln(a + 1) + 4\ln2 - 5\ln3.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_75540 (a : ℝ) (ha : 0 < a) :
  16 * (a + 2)^4 * (2 * a + 1) ≥ 243 * (a + 1)^4   :=  by sorry

Source

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

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