∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] (f : α → β)
  (hf : Continuous f) (K : TopologicalSpace.NonemptyCompacts α),
  (TopologicalSpace.NonemptyCompacts.map f hf K).toCompacts = TopologicalSpace.Compacts.map f hf K.toCompacts