∀ {B : Type u_2} {F : Type u_3} {Z : Type u_1} [inst : TopologicalSpace B] [inst_1 : TopologicalSpace F] {proj : Z → B}
  (e : Pretrivialization F proj) (s : Set B) [inst_2 : Nonempty (↑s → F → ↑(proj ⁻¹' s))],
  ∀ x ∈ Prod.map Subtype.val id ⁻¹' e.target,
    (if h : (↑x.1, x.2) ∈ e.target then ⟨e.invFun (↑x.1, x.2), ⋯⟩
      else Classical.arbitrary (↑s → F → ↑(proj ⁻¹' s)) x.1 x.2) ∈
      Subtype.val ⁻¹' e.source