lean_workbook_plus_32636

Proved

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

For all real numbers $a,b,c$ with $0 < a,b,c < 1$ is: $\sqrt{abc}+\sqrt{(1-a)(1-b)(1-c)}<3$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32636 (a b c : ℝ) (ha : 0 < a ∧ a < 1) (hb : 0 < b ∧ b < 1) (hc : 0 < c ∧ c < 1) :  Real.sqrt (a * b * c) + Real.sqrt ((1 - a) * (1 - b) * (1 - c)) < 3   :=  by sorry

Source

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

View graph