∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {F : CategoryTheory.Pseudofunctor B CategoryTheory.Cat}
  (P : F.ObjectProperty) [inst_1 : P.IsClosedUnderMapObj] {X Y : B} (f : X ⟶ Y),
  (P.fullsubcategory.map f).toFunctor = P.map f