∀ {B : Type u_2} {F : Type u_3} {Z : Type u_1} [inst : TopologicalSpace B] [inst_1 : TopologicalSpace F] {proj : Z → B}
  {s : Set B} (e : Bundle.Pretrivialization F fun z => proj ↑z) [inst_2 : Nonempty (Z → F)],
  ∀ x ∈ Subtype.val '' e.source,
    ↑(e.invFun (if h : proj x ∈ s then ↑e ⟨x, h⟩ else (proj x, Classical.arbitrary (Z → F) x))) = x