{α : Type u_2} →
  {β : Type u_3} →
    [inst : Preorder α] →
      [inst_1 : Preorder β] →
        {l : α → β} →
          {u : β → α} →
            (choice : (x : α) → u (l x) ≤ x → β) →
              GaloisConnection l u →
                (∀ (x : β), x ≤ l (u x)) → (∀ (a : α) (h : u (l a) ≤ a), choice a h = l a) → GaloisInsertion l u