lean_workbook_plus_76137

Proved

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

Suppose $a,b,c$ are the sides of a triangle. Prove or disprove $a(b+c-a)^2+b(a+c-b)^2+c(a+b-c)^2 \geq 3abc.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76137 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a * (b + c - a) ^ 2 + b * (a + c - b) ^ 2 + c * (a + b - c) ^ 2 ≥ 3 * a * b * c   :=  by sorry

Source

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

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