lean_workbook_plus_13918

Proved

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

Prove that for $a,b,c$ positive reals\n\n $a^2+b^2+c^2+ab+bc+ca \geq \sqrt{2(ab(a+b)+bc(b+c)+ca(c+a))(a+b+c)}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13918 :  ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → a^2 + b^2 + c^2 + a * b + b * c + c * a ≥ Real.sqrt (2 * (a * b * (a + b) + b * c * (b + c) + c * a * (c + a)) * (a + b + c))   :=  by sorry

Source

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

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