∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {homRel : HomRel C}
  {W : CategoryTheory.MorphismProperty C},
  homRel.FactorsThroughLocalization W →
    ∀ {E : Type u_4} [inst_1 : CategoryTheory.Category.{u_3, u_4} E] (F : CategoryTheory.Functor C E),
      W.IsInvertedBy F → ∀ (x x_1 : C) (f g : x ⟶ x_1), homRel f g → F.map f = F.map g