∀ {X Y : Type u} [inst : Group X] [inst_1 : TopologicalSpace X] [inst_2 : IsTopologicalGroup X]
  [inst_3 : CompactSpace X] [inst_4 : TotallyDisconnectedSpace X] [inst_5 : Group Y] [inst_6 : TopologicalSpace Y]
  [inst_7 : IsTopologicalGroup Y] [inst_8 : CompactSpace Y] [inst_9 : TotallyDisconnectedSpace Y] (f : X →ₜ* Y) (x : X),
  (ProfiniteGrp.Hom.hom (ProfiniteGrp.ofHom f)) x = f x