∀ {X : Type u_1} {Y : Type u_3} {Z : Type u_5} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] (e : OpenPartialHomeomorph X Y) {f : Y → Z} {x : Y},
  x ∈ e.target → (ContinuousAt f x ↔ ContinuousAt (f ∘ ↑e) (↑e.symm x))