Prove2Me

lean_workbook_plus_76084

Proved

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

If a,b,c>0,a2+b2+c2+abc=4a,b,c>0,a^2+b^2+c^2+abc=4 then: \n 3abc(a+b+c)≤8+abc3\sqrt{abc}(a+b+c)\le 8+abc

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_76084 (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) : 3 * Real.sqrt (a * b * c) * (a + b + c) ≤ 8 + a * b * c   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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