lean_workbook_plus_27718

Proved

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

If $a,b,c,d$ are real numbers all greater than1 then prove that $8(abcd+1) > (1+a)(1+b)(1+c)(1+d)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27718 (a b c d : ℝ) (hab : 1 < a) (hbc : 1 < b) (hcd : 1 < c) (hda : 1 < d) : 8 * (a * b * c * d + 1) > (1 + a) * (1 + b) * (1 + c) * (1 + d)   :=  by sorry

Source

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

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