lean_workbook_plus_18379

Proved

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

Let $a, b, c$ be positive real numbers such that $a^2+b^2+c^2+abc=4$ . Prove that \n $2\sqrt{2-abc}+abc\geq a+b+c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18379 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a^2 + b^2 + c^2 + a * b * c = 4) : 2 * Real.sqrt (2 - a * b * c) + a * b * c ≥ a + b + c   :=  by sorry

Source

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

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