lean_workbook_plus_70728

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that for real $a < b < c < d$ is $(a+b+c+d)^2 - 8(ac + bd) > 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_70728 (a b c d : ℝ) (h₁ : a < b ∧ b < c ∧ c < d) :  (a + b + c + d) ^ 2 - 8 * (a * c + b * d) > 0   :=  by sorry

Source