∀ {α : Type u_1} [inst : LT α] [Std.Asymm fun x1 x2 => x1 < x2] [Std.Trichotomous fun x1 x2 => x1 < x2]
  {xs ys : Array α},
  xs ≤ ys ↔
    xs = ys.take xs.size ∨
      ∃ i, ∃ (h₁ : i < xs.size) (h₂ : i < ys.size), (∀ (j : ℕ) (hj : j < i), xs[j] = ys[j]) ∧ xs[i] < ys[i]