A quadratic product bounds a product of two symmetric sums

Proved

WorkbookSource.base_38201

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

lean-workbooksource-checked

Prove that $4(a^2+1)(b^2+1)(c^2+1)\ge 3(ab+bc+ca)(a+b+c)$

Source: InternLM Lean-Workbook, record lean_workbook_38201 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38201 (a b c : ℝ) : 4 * (a^2 + 1) * (b^2 + 1) * (c^2 + 1) ≥ 3 * (a * b + b * c + c * a) * (a + b + c)  :=  by sorry

Source