∀ {α : Type u_1} {n : ℕ} [inst : LT α] [Std.Asymm fun x1 x2 => x1 < x2] [Std.Trichotomous fun x1 x2 => x1 < x2]
  [Trans (fun x1 x2 => ¬x1 < x2) (fun x1 x2 => ¬x1 < x2) fun x1 x2 => ¬x1 < x2] {xs ys zs : Vector α n},
  xs ≤ ys → ys ≤ zs → xs ≤ zs