{B : Type u_1} →
  {F : Type u_2} →
    {Z : Type u_4} →
      [inst : TopologicalSpace B] →
        [inst_1 : TopologicalSpace F] →
          {proj : Z → B} →
            Bundle.Pretrivialization F proj →
              (s : Set B) → [Nonempty (↑s → F → ↑(proj ⁻¹' s))] → Bundle.Pretrivialization F (s.restrictPreimage proj)