Prove2Me

lean_workbook_plus_18172

Proved

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

Prove that f(a,b,c)=15(a3+b3+c3+(ab+bc+ca)(a+b+c))+9abc−7(a+b+c)3≥0∀a,b,c≥0f(a,b,c)=15(a^{3}+b^{3}+c^{3}+(ab+bc+ca)(a+b+c))+9abc-7(a+b+c)^{3}\geq 0\forall a,b,c\geq 0.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_18172 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 15 * (a ^ 3 + b ^ 3 + c ^ 3 + (a * b + b * c + c * a) * (a + b + c)) + 9 * a * b * c - 7 * (a + b + c) ^ 3 ≥ 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

View graph