A pairwise product bound under a quadratic-factor product constraint

Proved

WorkbookSource.base_12499

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

lean-workbooksource-checked

With $(a^2+1)(b^2+1)(c^2+1)=64$ , prove that: $ab+bc+ca\le 9$

Source: InternLM Lean-Workbook, record lean_workbook_12499 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12499 (a b c : ℝ) (h : (a^2 + 1) * (b^2 + 1) * (c^2 + 1) = 64) :
 a * b + b * c + c * a ≤ 9  :=  by sorry

Source