lean_workbook_plus_69158

Proved

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

For all real numbers $a,b,c$ : $ab+bc+ca\leq a^{2}+b^{2}+c^{2}\Leftrightarrow 3(ab+bc+ca)\leq (a+b+c)^{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_69158 : ∀ a b c : ℝ, a * b + b * c + c * a ≤ a ^ 2 + b ^ 2 + c ^ 2 ↔ 3 * (a * b + b * c + c * a) ≤ (a + b + c) ^ 2   :=  by sorry

Source

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

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