A three-variable product inequality

Proved

WorkbookSource.problem_773

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

inequalitieslean-workbooksource-checked

For all real $a,b,c$ ,

(a^2+1)(b^2+1)(c^2+1)\ge(abc-1)^2.

Source: InternLM Lean-Workbook, record lean_workbook_773 (Apache-2.0). The complete source proposition is preserved.

Preamble

import Mathlib

Formal statement

theorem WorkbookSource.problem_773 (a b c : ℝ) : (a^2 + 1) * (b^2 + 1) * (c^2 + 1) ≥ (a * b * c - 1)^2  :=  by sorry

Source