lean_workbook_plus_64149

Proved

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

Suppose $a, b, c$ are the three sides of a triangle. Prove that $a^3+b^3+2(a+b)c^2 \ge c^3 + 2(a^2+b^2)c+abc$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64149 (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 + 2 * (a + b) * c^2 ≥ c^3 + 2 * (a^2 + b^2) * c + a * b * c   :=  by sorry

Source

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

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