lean_workbook_plus_43939

Proved

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

Prove that $(ab+bc+ca-1)^{2} \leq(a^{2} +1)(b^{2}+1)(c^{2}+1)$ for all real numbers $a, b$ and $c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_43939 : ∀ a b c : ℝ, (a * b + b * c + c * a - 1) ^ 2 ≤ (a ^ 2 + 1) * (b ^ 2 + 1) * (c ^ 2 + 1)   :=  by sorry

Source