∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [T1Space X] [inst_2 : DecidableEq X]
  [inst_3 : TopologicalSpace Y] {f : X → Y} {s : Set X} {x x' : X} {y : Y},
  x' ≠ x → (ContinuousWithinAt (Function.update f x y) s x' ↔ ContinuousWithinAt f s x')