A mixed product bound with two moment constraints

Proved

WorkbookSource.base_7713

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

lean-workbooksource-checked

Let $a,b,c,d$ be reals such that $a+b+c+d=4$ and $a^2+b^2+c^2+d^2=18.$ Prove that $ab-2cd \leq \frac{74}{5}$

Source: InternLM Lean-Workbook, record lean_workbook_7713 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7713 (a b c d : ℝ) (h₁ : a + b + c + d = 4) (h₂ : a^2 + b^2 + c^2 + d^2 = 18) : a * b - 2 * c * d ≤ 74 / 5  :=  by sorry

Source