∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set Y},
  IsDiscrete s → ContinuousOn f (f ⁻¹' s) → (∀ (x : Y), IsDiscrete (f ⁻¹' {x})) → IsDiscrete (f ⁻¹' s)