Prove2Me

lean_workbook_plus_6337

Proved

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

Determine if the expression 14((a−b)2+(b−c)2+(c−a)2)((a−b)2(a+b)+(b−c)2(b+c)+(c−a)2(c+a))\frac{1}{4} \left((a -b)^2+(b-c)^2+(c-a)^2\right)\left((a-b)^2(a+b)+(b-c)^2(b+c)+(c-a)^2(c+a)\right) is greater than or equal to zero for all positive real numbers a,b,ca, b, c.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_6337 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 0 ≤ (1 / 4) * ((a - b) ^ 2 + (b - c) ^ 2 + (c - a) ^ 2) * ((a - b) ^ 2 * (a + b) + (b - c) ^ 2 * (b + c) + (c - a) ^ 2 * (c + a))   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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