∀ {α : Type u} [inst : LinearOrder α] {a : α} {as m : List α},
  List.IsChain (fun x1 x2 => x1 > x2) (a :: as) →
    List.IsChain (fun x1 x2 => x1 > x2) m → m ≤ as → List.IsChain (fun x1 x2 => x1 > x2) (a :: m)