∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {D : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_3, u_4} D] {S : D} {T : CategoryTheory.Functor C D}
  [inst_2 : CategoryTheory.Limits.HasFiniteLimits C] [inst_3 : CategoryTheory.Limits.PreservesFiniteLimits T]
  (A : CategoryTheory.StructuredArrow S T)
  (P : { P // ∃ q, CategoryTheory.CategoryStruct.comp q (T.map P.arrow) = A.hom }),
  ↑((fun P => ⟨CategoryTheory.StructuredArrow.projectSubobject P, ⋯⟩)
        ((fun P => CategoryTheory.StructuredArrow.liftSubobject ↑P ⋯) P)) =
    ↑P