lean_workbook_plus_47285

Proved

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

If $a,b,c$ are sides of a triangle, then \n\n $a^3 + b^3 + c^3 - 3abc-2(c-b)^3$ \n\n $=\frac{(a+9b-c)(c-a)^2+3(a+b-c)(c+a-2b)^2}{4}\geq0.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_47285 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a^3 + b^3 + c^3 - 3 * a * b * c - 2 * (c - b)^3 ≥ 0   :=  by sorry

Source

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

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