Cartesian_Product_Distributes_over_Union

import Mathlib.Data.Set.Prod

theorem Cartesian_Product_Distributes_over_Union {α : Type _} {β : Type _} (A : Set α) (B C : Set β) : A ×ˢ (B ∪ C) = (A ×ˢ B) ∪ (A ×ˢ C) := by sorry