Prove2Me

lean_workbook_plus_23360

Proved

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

Suppose a,b,c are sides of triangle. Prove that:\n

a2(b+c−a)+b2(a+c−b)+c2(a+b−c)≤ 3abca^2 (b + c - a) + b^2 (a+ c - b) + c^2 (a + b - c) \le\ 3 a b c
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_23360 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a^2 * (b + c - a) + b^2 * (a + c - b) + c^2 * (a + b - c) ≤ 3 * a * b * c   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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