lean_workbook_plus_41824

Proved

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

Note that upon expanding and cancellation it remains to prove $a^4+a \ge a^3+a$ which can be rewritten as $a^3(a)+1(1) \ge a^3(1)+1(a)$ which is trivial by Rearrangement inequality because the pairs $(a^3,1) , (a,1)$ are because $a \ge 1 \iff a^3 \ge 1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41824  (a : ℝ)
  (h₀ : 1 ≤ a) :
  a^4 + a ≥ a^3 + 1   :=  by sorry

Source

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

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