lean_workbook_plus_1402

Proved

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

Let $a,b,c \in [1,2]$ . Prove that $2(ab+bc+ca) \geq a^2+b^2+c^2+a+b+c$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1402 {a b c : ℝ} (ha : 1 ≤ a ∧ a ≤ 2) (hb : 1 ≤ b ∧ b ≤ 2) (hc : 1 ≤ c ∧ c ≤ 2) : 2 * (a * b + b * c + c * a) ≥ a ^ 2 + b ^ 2 + c ^ 2 + a + b + c   :=  by sorry

Source

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

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