∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  {F : CategoryTheory.Functor C D} {J : CategoryTheory.Precoverage D} {X : C} {R : CategoryTheory.Presieve X},
  R ∈ (CategoryTheory.Precoverage.comap F J).coverings X ↔ CategoryTheory.Presieve.map F R ∈ J.coverings (F.obj X)