lean_workbook_plus_75079

Proved

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

With $k=1$ , we have: $(1-a)(1-b)(1-c)\ge 0 \leftrightarrow 1+ab+bc+ca \ge a+b+c+abc$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_75079 : ∀ a b c : ℝ, (1 - a) * (1 - b) * (1 - c) ≥ 0 ↔ 1 + a * b + b * c + c * a ≥ a + b + c + a * b * c   :=  by sorry

Source