∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {J : CategoryTheory.Precoverage C} {T : C}
  [J.IsStableUnderComposition] (E : J.ZeroHypercover T) (F : (i : E.I₀) → J.ZeroHypercover (E.X i)),
  (CategoryTheory.Presieve.ofArrows (fun p => (F p.fst).X p.snd) fun x =>
      CategoryTheory.CategoryStruct.comp ((F x.fst).f x.snd) (E.f x.fst)) ∈
    J.coverings T