∀ {X : TopCat} (x : ↑X) (U : Set ↑X) (p : IsOpen U)
  (q : (CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.id X)) x ∈ { carrier := U, is_open' := p }),
  (TopologicalSpace.OpenNhds.map (CategoryTheory.CategoryStruct.id X) x).obj ⟨{ carrier := U, is_open' := p }, q⟩ =
    ⟨{ carrier := U, is_open' := p }, q⟩