Prove2Me

lean_workbook_plus_61082

Proved

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

If a,b,c>0 a, b, c > 0 , prove that\n\n1. 4(a3+b3)≥(a+b)3 4(a^3 + b^3)\ge (a + b)^3 \n\n2. 9(a3+b3+c3)≥(a+b+c)3 9(a^3 + b^3 + c^3) \ge (a + b + c)^3

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_61082 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → (4 * (a ^ 3 + b ^ 3) ≥ (a + b) ^ 3 ∧ 9 * (a ^ 3 + b ^ 3 + c ^ 3) ≥ (a + b + c) ^ 3)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

View graph