{B : Type u_2} →
  {F : Type u_3} →
    {E : B → Type u_5} →
      [inst : TopologicalSpace B] →
        [inst_1 : TopologicalSpace F] →
          [inst_2 : (x : B) → TopologicalSpace (E x)] →
            (pretrivializationAtlas : Set (Bundle.Pretrivialization F Bundle.TotalSpace.proj)) →
              (pretrivializationAt : B → Bundle.Pretrivialization F Bundle.TotalSpace.proj) →
                (∀ (x : B), x ∈ (pretrivializationAt x).baseSet) →
                  (∀ (x : B), pretrivializationAt x ∈ pretrivializationAtlas) →
                    (∀ e ∈ pretrivializationAtlas,
                        ∀ e' ∈ pretrivializationAtlas,
                          ContinuousOn (↑e ∘ ↑e'.symm) (e'.target ∩ ↑e'.symm ⁻¹' e.source)) →
                      (∀ (b : B), Topology.IsInducing (↑(pretrivializationAt b) ∘ Bundle.TotalSpace.mk b)) →
                        FiberPrebundle F E