∀ {α : Type u_1} {β : Type u_2} [inst : Add α] [inst_1 : Preorder α] [inst_2 : Preorder β] {f g : β → α} {s : Set β}
  [AddLeftStrictMono α] [AddRightStrictMono α],
  StrictAntiOn f s → StrictAntiOn g s → StrictAntiOn (fun x => f x + g x) s