{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.IsCofilteredOrEmpty C] →
      (n : ℕ) →
        (X : (k : ℕ) → k < n → (t : Type (max v w)) × (t → C)) →
          CategoryTheory.IsCofiltered.CofilteredClosureSmall.InductiveStep✝ n X → C