Prove2Me

lean_workbook_plus_65543

Proved

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

sujun1993's Identity : 7(∑a2)2−12∑a4+(∑a)[5∑a3−5∑a2(b+c+d)+6∑bcd]=2[(a−b)2(c−d)2+(a−c)2(b−d)2+(a−d)2(b−c)2]≥0. 7\left(\sum{a^2}\right)^2 - 12\sum{a^4} +\left(\sum{a}\right)\left[5\sum{a^3} - 5\sum{a^2(b + c + d) + 6\sum{bcd}}\right] = 2\left[(a-b)^2(c-d)^2+(a-c)^2(b-d)^2+(a-d)^2(b-c)^2\right]\geq0.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_65543 {a b c d : ℝ} : 7 * (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) ^ 2 - 12 * (a ^ 4 + b ^ 4 + c ^ 4 + d ^ 4) + (a + b + c + d) * (5 * (a ^ 3 + b ^ 3 + c ^ 3 + d ^ 3) - 5 * (a ^ 2 * (b + c + d) + b ^ 2 * (c + d + a) + c ^ 2 * (d + a + b) + d ^ 2 * (a + b + c)) + 6 * (b * c * d + a * c * d + a * b * d + a * b * c)) = 2 * ((a - b) ^ 2 * (c - d) ^ 2 + (a - c) ^ 2 * (b - d) ^ 2 + (a - d) ^ 2 * (b - c) ^ 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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