∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] (f f_1 : α → β)
  (e_f : f = f_1) (hf : Continuous f) (K K_1 : TopologicalSpace.NonemptyCompacts α),
  K = K_1 → TopologicalSpace.NonemptyCompacts.map f hf K = TopologicalSpace.NonemptyCompacts.map f_1 ⋯ K_1