lean_workbook_plus_75820

Proved

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

For $0<a,b,c,d<1$ . Prove that: $(1-a)(1-b)(1-c)(1-d)>1-a-b-c-d$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_75820 (a b c d : ℝ) (hab : 0 < a ∧ a < 1) (hbc : 0 < b ∧ b < 1) (hcd : 0 < c ∧ c < 1) (hded : 0 < d ∧ d < 1) : (1 - a) * (1 - b) * (1 - c) * (1 - d) > 1 - a - b - c - d   :=  by sorry

Source

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

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