∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C}
  {P : CategoryTheory.ObjectProperty J.Point} [CategoryTheory.LocallySmall.{w, v, u} C]
  [CategoryTheory.HasSheafify J (Type w)],
  (∀ ⦃X : C⦄ (S : CategoryTheory.Sieve X),
      (∀ (Φ : P.FullSubcategory) (x : Φ.obj.fiber.obj X), ∃ Y g, ∃ (_ : S.arrows g), ∃ y, Φ.obj.fiber.map g y = x) →
        S ∈ J X) →
    P.IsConservativeFamilyOfPoints