A product of quadratic factors under a fixed sum

Proved

WorkbookSource.plus_64300

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

For $a,b,c \in \mathbb R$ such that $a+b+c=7$ . Prove: $(a^2+1)(b^2+1)(c^2+1)+30abc+15 \ge 0$

Source: InternLM Lean-Workbook, record lean_workbook_plus_64300 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_64300 (a b c : ℝ) (h : a + b + c = 7) : (a^2 + 1) * (b^2 + 1) * (c^2 + 1) + 30 * a * b * c + 15 ≥ 0   :=  by sorry

Source