A lower bound on four absolute values from pairwise products

Proved

WorkbookSource.base_878

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

lean-workbooksource-checked

Let $a,b,c,d$ be real numbers such that $ab+ac+ad+bc+bd+cd=-1.$ Prove that $|a|+|b|+|c|+|d|\geq 2.$

Source: InternLM Lean-Workbook, record lean_workbook_878 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_878 (a b c d : ℝ) (h : a * b + a * c + a * d + b * c + b * d + c * d = -1) : |a| + |b| + |c| + |d| ≥ 2  :=  by sorry

Source