Three quadratic factors bound twice the pairwise sum

Proved

WorkbookSource.plus_80171

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers . Prove that $(1+a^2)(1+b^2)(1+c^2)\ge 2 (ab+bc+ca)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_80171 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_80171 (a b c : ℝ) : (1 + a ^ 2) * (1 + b ^ 2) * (1 + c ^ 2) ≥ 2 * (a * b + b * c + c * a)   :=  by sorry

Source