∀ {α : Type u_2} {β : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  {B : Set (TopologicalSpace.Opens β)},
  TopologicalSpace.Opens.IsBasis B →
    ∀ {f : α → β} (h : Topology.IsInducing f),
      TopologicalSpace.Opens.IsBasis {x | ∃ U ∈ B, { carrier := f ⁻¹' ↑U, is_open' := ⋯ } = x}