∀ {C : Type uC} [inst : CategoryTheory.Category.{vC, uC} C] {D : Type uD} [inst_1 : CategoryTheory.Category.{vD, uD} D]
  {G : CategoryTheory.Functor C D} {K : CategoryTheory.GrothendieckTopology D},
  (∀ {U V : C} (f₁ f₂ : U ⟶ V),
      G.map f₁ = G.map f₂ →
        CategoryTheory.Sieve.functorPushforward G (CategoryTheory.Sieve.equalizer f₁ f₂) ∈ K (G.obj U)) →
    G.IsLocallyFaithful K