∀ {G : ProfiniteGrp.{u}} {H : Type v} [inst : TopologicalSpace H] [inst_1 : Group H] [inst_2 : IsTopologicalGroup H]
  (e : ↑G.toProfinite.toTop ≃ₜ* H), ProfiniteGrp.ofContinuousMulEquiv e = ProfiniteGrp.of H