Prove2Me

lean_workbook_plus_44050

Disproved

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

By Holder (a3+3)(b3+3)(2+(c+d)34)=(a^3+3)(b^3+3)\left(2+\frac{(c+d)^3}{4}\right)=\n=(a3+1+2)(1+b3+2)(1+1+(c+d)34)≥(a+b+c+d)3=(a^3+1+2)(1+b^3+2)\left(1+1+\frac{(c+d)^3}{4}\right)\geq(a+b+c+d)^3 .\nHence, it remains to prove that (c3+3)(d3+3)≥8+(c+d)3(c^3+3)(d^3+3)\geq8+(c+d)^3

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_44050 : ∀ c d : ℝ, (c^3 + 3) * (d^3 + 3) ≥ 8 + (c + d)^3   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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