Prove2Me

lean_workbook_plus_32736

Proved

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

Prove that (a+b+c)2≥2(a+b+c)+ab+bc+ca⇔a2+b2+c2+ab+bc+ca≥2(a+b+c)(a + b + c)^2 \geq 2(a + b + c) + ab + bc + ca \Leftrightarrow a^2 + b^2 + c^2 + ab + bc + ca \geq 2(a + b + c).

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_32736 (a b c : ℝ) : (a + b + c) ^ 2 ≥ 2 * (a + b + c) + a * b + b * c + c * a ↔ a ^ 2 + b ^ 2 + c ^ 2 + a * b + b * c + c * a ≥ 2 * (a + b + c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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