lean_workbook_plus_78856

Proved

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

Let $a,b,c$ be sides of a triangle. Show $-a^3 + a^2 b + a^2 c + a b^2 - 2 a b c + a c^2 - b^3 + b^2 c + b c^2 - c^3 \geq 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78856 {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 + a^2 * b + a^2 * c + a * b^2 - 2 * a * b * c + a * c^2 - b^3 + b^2 * c + b * c^2 - c^3 ≥ 0   :=  by sorry

Source

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

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