lean_workbook_plus_2689

Proved

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

Let: $a,b,c>0$ and $(a^{2}+1)(b^{2}+1)(c^{2}+1)=8$ . Prove that: $ab+bc+ac+abc\leq 4$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2689 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : (a^2 + 1) * (b^2 + 1) * (c^2 + 1) = 8) :
  a * b + b * c + c * a + a * b * c ≤ 4   :=  by sorry

Source

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

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