lean_workbook_plus_435

Proved

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

Prove that for non-negative real numbers $a, b, c$ , the following inequality holds: $(a^{2}+b^{2}-c^{2})(a-b)^{2}+(b^{2}+c^{2}-a^{2})(b-c)^{2}+(c^{2}+a^{2}-b^{2})(c-a)^{2}\geq 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_435 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a^2 + b^2 - c^2) * (a - b)^2 + (b^2 + c^2 - a^2) * (b - c)^2 + (c^2 + a^2 - b^2) * (c - a)^2 ≥ 0   :=  by sorry

Source

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

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