lean_workbook_plus_8521

Proved

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

If $a>0$ , $b>0$ and $c>0$ and $(a^2+b^2+c^2)^2>2(a^4+b^4+c^4)$ so $(a+b+c)(a+b-c)(a+c-b)(b+c-a)>0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8521 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2)^2 > 2 * (a^4 + b^4 + c^4) → (a + b + c) * (a + b - c) * (a + c - b) * (b + c - a) > 0   :=  by sorry

Source

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

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